Testing Experimental Anti-cancer Drug SLC-391 With an Approved Immunotherapy Drug, Pembrolizumab, for Advanced Lung Cancers

Inclusion Criteria: * The subject provides written informed consent. * Adults ≥ 18 years of age on day of signing informed consent. * Disease must be measurable per RECIST 1.1, as assessed by the Site(s) Investigator/radiologist. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in these lesions. * Subject has histologically or cytologically documented, locally advanced (Stage IIIB or IIIC) disease (not candidate for surgical resection, local therapies with curative intent, or definitive chemoradiation) or the subject has metastatic NSCLC (Stage IV). Staging will be based on the American Joint Committee on Cancer, Eighth Edition. Subjects with adenocarcinoma, large cell carcinoma, undifferentiated carcinoma, squamous carcinoma, or mixed histology are eligible. Subjects with a small cell component are not eligible. * Phase 1b Subjects additional eligibility criteria: 1. Subjects must have received a minimum of one prior systemic treatment for advanced unresectable or metastatic NSCLC and progressed following prior SOC. 2. Maximum of up to 4 prior lines of therapy in an advanced or metastatic setting is allowed. 3. Subjects who had disease recurrence or progression following neoadjuvant or adjuvant therapy or definitive chemoradiation therapy are eligible. 4. Subjects who received treatment with an approved/available targeted therapy for an actionable genomic alteration (including but not limited to EGFR, ALK, ROS1, KRAS, etc.) can participate if they have documented disease progression or were unable to tolerate the approved targeted therapy. Phase 1b Notes: * Targeted therapy for advanced setting is counted as a prior line of therapy. * Prior use of a PD(L)-1, anti-CTLA-4 (Cytotoxic T-lymphocyte associated protein 4) antibody, or any other antibody or drug that specifically targets immune checkpoint pathway is allowed and is counted as a prior line of therapy. * Neoadjuvant and adjuvant therapies initiated \< 12 months prior to the first dose of study drug(s) will be counted as one prior line of therapy for advanced setting. * Neoadjuvant and adjuvant therapies initiated ≥ 12 months prior to the first dose of study drug(s) are not counted as prior lines of therapy. * Maintenance therapy is not counted as a prior line of therapy. * Phase 2a Subjects additional eligibility criteria: Cohort 1: 1. Tumors must have PD-L1 expression (TPS ≥ 1% as determined by SOC). 2. Subjects are eligible to participate if they did not receive any prior therapy (SOC or investigational) or prior immunotherapy of any kind for advanced or metastatic disease. See Exclusion Criteria 1.0. 3. Subjects with disease recurrence or progression following neoadjuvant or adjuvant therapy or definitive chemoradiation therapy are eligible. 4. Prior adjuvant or neoadjuvant immunotherapy is allowed if completed more than 12 months before documented relapse. Cohort 2: 1. Subjects should have received at least 2 doses of an approved anti PD(L) 1 monoclonal antibody (mAb) in an advanced or metastatic setting. 2. Progressive disease should be documented during treatment or within 12 weeks from the last dose of anti-PD(L)-1 mAb. 3. Up to a maximum of 2 prior lines of approved cancer therapy in an advanced or metastatic setting, including an anti-PD(L)-1 mAb administered either as monotherapy or in combination with other therapies, is allowed. 4. Subjects who received treatment with an approved/available targeted therapy for an actionable genomic alteration (including but not limited to EGFR, ALK, ROS1, KRAS, etc.) can participate if they have documented disease progression or were unable to tolerate the approved targeted therapy. Only these subjects are allowed to receive up to a maximum of 3 prior lines of cancer therapy in an advanced or metastatic setting. 5. Subjects with disease recurrence or progression following neoadjuvant or adjuvant therapy or definitive chemoradiation therapy are eligible. Cohort 2 Notes: * Targeted therapy for advanced setting is counted as a prior line of therapy. * Maintenance therapy is not counted as a prior line of therapy. * Neoadjuvant and adjuvant therapies initiated \< 12 months prior to first dose of study drug(s) will be counted as one prior line of therapy for advanced setting. * Neoadjuvant and adjuvant therapies initiated ≥ 12 months prior to first dose of study drug(s) are not counted as prior lines of therapy. * Subject has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Life expectancy of at least 3 months. * An archival tumor tissue sample or newly obtained biopsy of a tumor lesion not previously irradiated must exist to participate in the study (Mandatory in Phase 2a but subjects in Phase 1b may be enrolled in the absence of a tumor tissue sample). Only core needle and/or excisional biopsy samples, from archival or fresh tissue, will be accepted in this study. * Adequate organ function as defined below must be met for subjects to participate in the study. Clinical laboratory specimens must be collected within 10 days prior to first dose of study drug(s): 1. Absolute neutrophil count (ANC) ≥ 1500/µL or ≥ 1.5 × 109/L (in the absence of growth factor support). 2. Platelets ≥ 100,000/µL or 100 × 109/L (in the absence of transfusion or growth factor support). 3. Hemoglobin ≥ 9 g/dL or ≥ 90 g/L (in the absence of transfusion). Note: Criteria must be met without packed red blood cell transfusion within the prior 2 weeks. Subjects can be on stable dose of erythropoietin (≥ approximately 3 months). 4. Creatinine Clearance (CCr) ≥ 50 mL/minute using the Cockcroft and Gault formula. Note: The Cockcroft and Gault formula (1973): CCr = (\[{140 - age} × weight\]/\[72 × SCr\]) × 0.85 (if female); where CCr = mL/minute; age = years; weight = kg; SCr (serum creatinine) = mg/dL. 5. Total bilirubin ≤ 1.5 × upper limit of normal (ULN) (unless a diagnosis of Gilbert's syndrome in which case ≤ 3 × ULN) OR direct bilirubin ≤ 1 × ULN for participants with total bilirubin \>1.5 × ULN. 6. Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 × ULN (≤ 5× ULN for subjects with liver metastases). 7. International normalized ratio (INR) or prothrombin time (PT) ≤ 1.5 × ULN; if the subject is receiving anticoagulant therapy PT or INR should be within the therapeutic range of the intended use of anticoagulants. 8. Activated partial thromboplastin time/partial thromboplastin time (aPTT/PTT) ≤ 1.5 × ULN; if the subject is receiving anticoagulant therapy PTT should be within the therapeutic range of intended use of anticoagulants. Note: Low molecular weight heparin, warfarin (INR monitoring required), direct oral anticoagulants, and drugs in the anticoagulant class (e.g., Lovenox \[enoxaparin\]) administered for deep vein thrombosis are permitted. * Women who are not of childbearing potential must be documented and will not be tested for pregnancy or required to utilize contraception if they meet one or more of the following definitions of non-childbearing potential: 1. Amenorrheic for \> 2 years without a hysterectomy and oophorectomy, and a follicle stimulating hormone (FSH) value in the postmenopausal range upon screening evaluation. 2. Post-hysterectomy, bilateral oophorectomy, or tubal ligation. Tubal ligation should be confirmed with medical records of the actual procedure. * 12\. Women of childbearing potential (WOCBP) must have a negative pregnancy test (serum) within 72 hours prior to first dose of study drug(s) and meet the following criteria throughout the study, starting with the screening visit through 120 days after the last dose of study drug(s) (or 30 days if new cancer therapy is initiated): 1. Agrees to follow contraceptive guidance throughout the study as per protocol. 2. Willing to use 2 highly effective birth control methods throughout the study. The 2 birth control methods can be either 2 barrier methods or a barrier method plus a hormonal method to prevent pregnancy. Refer to Appendix 4 for complete list of acceptable birth control methods. 3. Refrain from egg donation. Note: If there is any question that a subject will not reliably comply with the requirements for contraception, that subject should not be enrolled. * Male subjects must agree to use an acceptable method of contraception and refrain from sperm donation throughout the study: from screening, during the treatment period, and for at least 120 days after the last dose of study drug(s) (or 30 days if new cancer therapy is initiated). * Willing and able to participate in blood sampling and all other required study procedures. Exclusion Criteria: * Phase 2a - Cohort 1 (only) exclusion criteria: 1. Subjects have tumors that have actionable genomic alterations with approved targeted therapy in first line setting are not eligible to participate. 2. Subjects are not eligible if they received any prior therapy (SOC or investigational) for advanced or metastatic disease including chemotherapy, targeted therapy, or immunotherapy of any kind such as the following: pembrolizumab, an anti-PD(L)-1 or anti-programmed death ligand 2 (PD-L2) agent, or an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g., CTLA4, OX40 (Tumor necrosis factor receptor superfamily, member 4), CD137(Tumor necrosis factor receptor superfamily member 9)). * Undergone prior treatment with a known AXL inhibitor such as bemcentinib (see Section 8.2.2 for full list of AXL inhibitors). * Received prior systemic anticancer therapy within 5 half-lives or 3 weeks, whichever is shorter, prior to starting the first dose of study drug(s). Examples of prior systemic anticancer therapy includes cytotoxic agents, targeted therapy such as small molecules, mAbs and hormonal therapy etc.. * Received immunotherapies \[including but not limited to PD(L)-1 inhibitors, etc.\] within 4 weeks prior to starting the first dose of study drug(s). * Received prior radiotherapy within 2 weeks of the first dose of study drug(s) or had a history of radiation pneumonitis. Note: Subjects must have recovered from all radiation-related toxicities and not require corticosteroids. A 1 week washout is permitted following palliative radiation (≤ 2 weeks of radiotherapy) for non-central nervous system (CNS) disease. * Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study drug(s). Note: Subjects who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent, follow-up is primarily non-invasive, and the subject can comply with protocol requirements. * Has not recovered to ≤ Grade 1 or to baseline from prior cancer therapy toxicity. Note: Subject with ≤ Grade 2 neuropathy may be an exception to this criterion and may qualify for the study after discussion with Sponsor. Subjects with endocrine-related AEs ≤ Grade 2 requiring treatment or hormone replacement may be eligible after discussion with Sponsor. Note: Toxic effects also include laboratory results that have not resolved to ≤ Grade 1. Subjects with ≤ Grade 2 alopecia are an exception to this criterion. * Has not adequately recovered from major surgery and/or complications from the procedure prior to the first dose of study drug(s). * Pulmonary hemorrhage or hemoptysis \> 2.5 mL blood within 6 weeks of screening (or within 2 weeks if the source of bleeding is treated). * Received a live or live-attenuated vaccine within 30 days prior to the first dose of study drug(s). Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacille Calmette-Guerin, and typhoid vaccine. Seasonal influenza vaccines are generally killed virus vaccines and are permitted; however, intranasal influenza vaccines (e.g., Flu-Mist®) are live-attenuated vaccines and are not allowed. Note: The administration of killed vaccines, mRNA vaccines, and DNA vaccines is allowed. * Has an active diagnosis of immunodeficiency or is receiving systemic steroid therapy (exceeding 10 mg daily of prednisone equivalent) or has received any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug(s). * Has active autoimmune disease which required systemic treatment in past 2 years (i.e., with use of disease modifying agents, corticosteroids, or immunosuppressive drugs). Note: Hormone therapy (e.g., thyroxine, insulin, or corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed. * Known additional malignancy that is progressing or has required active treatment within the past 2 years. Note: Subjects with curatively treated basal or squamous cell carcinoma of the skin (non-melanoma skin cancer), cervical or vaginal intra-epithelial neoplasia, non-invasive breast cancer in situ, or localized prostate cancer with a prostate-specific antigen level of \< 4 ng/mL (µg/L) at screening are not excluded. Subjects with other curatively treated malignancies who have had a \> 2-year disease-free interval and whose natural history or treatment does not have the potential to interfere with investigational agents (e.g., hormone maintenance) may be enrolled after approval by the Medical Monitor/Sponsor. * Known active CNS metastases and/or carcinomatous meningitis. Subjects with adequately treated brain metastases may participate provided they meet the following criteria: 1. Are radiologically stable (no progression) for at least 4 weeks as documented by screening computed tomography (CT) or magnetic resonance imaging (MRI) scan. 2. Clinically stable. 3. No evidence of new or enlarging brain metastases. Does not require steroids for at least 14 days before starting first dose of study drug(s) (anticonvulsants at a stable dose are allowed). Low dose steroids equivalent of prednisone ≤ 10 mg orally once a day is allowed. 4. No history of intracranial or spinal cord hemorrhage. 5. No evidence of significant vasogenic edema. * Severe hypersensitivity (≥ Grade 3) to pembrolizumab or SLC-391 and/or any excipients. * A history of non-infectious pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease. * A known history of human immunodeficiency virus (HIV) infection (HIV 1/2 antibodies). No HIV testing is required unless mandated by the local health authority. * Known history of Hepatitis B (Anti-HBc and HBsAg reactive) or known active Hepatitis C virus (RNA, qualitative) infection. Note: No testing for Hepatitis B or C is required unless mandated by a local health authority. * A history or current evidence of any severe acute or chronic medical or psychiatric condition that requires treatment, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject, in the opinion of the Principal Investigator (PI; also referred to as Investigator). Examples include, but are not limited to, active uncontrolled infection (including tuberculosis \[TB\]) requiring systemic therapy, transfusion dependent anemia, recent (within 90 days) stroke or myocardial infarction, unstable angina, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, symptomatic congestive heart failure (New York Heart Association class ≥ III/IV), and recent severe Coronavirus disease 2019 (COVID-19). Note: TB testing is required for subjects recently exposed to persons with active TB or who have traveled recently to areas where TB is endemic. * Systolic blood pressure (BP) ≥ 160 mmHg or diastolic BP ≥100 mmHg. * Has a corrected QT interval by Fridericia (QTcF) ≥ 470 msec. Note: Apply the Fridericia QT correction to calculate QTcF using the following formula: QTcF = QT/RR1/3 where QT = the time between the start of the QRS complex and the end of the T wave and RR = the time between the start of one QRS complex and the start of the next QRS complex. Note: If a subject has a prolonged QT interval and the prolongation is deemed to be due to a pacemaker as deemed by the Investigator (i.e., the subject otherwise has no cardiac abnormalities), the subject may be eligible to participate in the study following discussion with the Sponsor. * History or presence of sustained or symptomatic bradycardia (≤ 55 bpm), left bundle branch block, ventricular arrhythmia excluding premature ventricular contractions, or uncontrolled ventricular arrhythmia. Subjects with a supraventricular arrhythmia requiring medical treatment and a normal ventricular rate are eligible. * Psychological, familial, sociological, or geographical conditions including known psychiatric or substance abuse disorder that could interfere with the subject's ability to provide informed consent, comply with the protocol, or interfere with the interpretation of the study results. * Inability to swallow oral medication and/or the presence of active gastrointestinal (GI) disease and/or other GI conditions, including bowel resection, that is expected to interfere significantly with the absorption, distribution, metabolism, or excretion of oral SLC-391 therapy. * Received radiation therapy to the lung that is \> 30 Gy within 6 months of the first dose of study drug(s). * Had an allogenic tissue, marrow, or solid organ transplant. * Females who are pregnant or nursing. Note: SLC reserves the right to deny any subject enrollment based upon potential safety concern(s) or factors that could confound the study results. Note: The Investigator or licensed, medically qualified Sub-Investigator must review and confirm eligibility prior to the first dose of study drug(s).