Pembrolizumab (Immunotherapy Drug) in Combination With Guadecitabine and Mocetinostat (Epigenetic Drugs) for Patients With Advanced Lung Cancer.

Inclusion Criteria: * Patient must be capable, willing, and able to provide written, informed consent * Age ≥ 18 years old * Histologically-confirmed stage IIIb or IV NSCLC by the enrolling institution * Patients must have progressed on treatment with an anti-PD1/PD-L1 monoclonal antibody (mAb) administered either as monotherapy, or in combination with other checkpoint inhibitors or other therapies. PD-1/PD-L1 treatment progression is defined by meeting all of the following criteria: a. Has received at least 2 doses of an approved anti-PD-1/PD-L1 mAb b. Has demonstrated disease progression after PD-1/PD-L1 as defined by RECIST v1.1 (if treatment received as part of a clinical trial with formal RECIST reads performed) or a combination of clinical AND radiologic evidence of progression, as determined by the treating investigator. The initial evidence of disease progression (PD) should ideally be confirmed by a second assessment no less than 4 weeks from the date of the first documented PD, unless there is rapid clinical progression such that follow up imaging is infeasible. i. Note: Second imaging for confirmation of PD can be waived in rapidly progressing patients after consultation with the Sponsor/PI. Progressive disease has been documented within 24 weeks from the last dose of anti-PD-1/PD-L1 mAb. * Measurable by RECIST v1.1 (those undergoing pre-treatment resection must have imaging assessment after resection to determine measurability) a. Previously irradiated sites of tumor may be considered measurable if there is radiographic progression at that site subsequent to the time of completing radiation. * Have a safely biopsiable tumor lesion and be willing to undergo a pre-treatment and ontreatment core biopsy 1. Pretreatment tissue should be collected via core biopsy, ideally of a non-target lesion. 2. Patients may not have intervening systemic anti-cancer therapy between the time of pre-treatment biopsy/resection and initiating study treatment. * ECOG performance status of 0-1. * Adequate hematologic, renal, and/or hepatic function (following criteria must be met within 28 days of C1D1): a. ANC ≥ 1,500/mm3 (≥ 1. 5 × 10\^9/L) b. Hemoglobin ≥ 9.0 g/dL c. Platelet count ≥ 100,000/ul (≥ 100,000 per mm3) d. Serum creatinine ≤ 1.5 x ULN OR, for subjects with creatinine levels \>1.5 x ULN, an estimated creatinine clearance of ≥ 40 mL/min calculated using the Cockcroft and Gault formula ((140-Age) • Mass (kg)/(72 • creatinine mg/dL); multiply by 0.85 if female) e. Total bilirubin ≤ 1.5 x ULN OR, for subjected with total bilirubin levels \>1.5 x ULN, a direct bilirubin ≤ ULN f. AST and ALT ≤ 3 x UNL (unless elevated transaminases are felt to be directly related to metastatic disease involving the liver, in which case AST and ALT must be ≤ 5x ULN) * Women of childbearing potential (WOCBP) † must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 28 days of C1D1. † A woman of childbearing potential is a sexually mature female who: has not undergone a hysterectomy or bilateral oophorectomy; or has not been naturally postmenopausal for at least 24 consecutive months (i.e. has had menses at any time in the preceding 24 consecutive months). * Effective contraception: 1. Women of childbearing potential must agree to practice 2 effective methods of contraception from the time of signing the informed consent form through 120 days after the last dose of study therapy, or agree to completely abstain from heterosexual intercourse. 2. Male subjects, even if surgically sterilized (i.e., status post vasectomy) must agree to 1 of the following: practice effective barrier contraception during the entire study treatment period and through 120 days after the last dose of study therapy, or agree to completely abstain from heterosexual intercourse. * Willing to comply with clinical trial instructions and requirements, including mandatory biopsies. Exclusion Criteria: * Presence of targetable EGFR mutations or ALK re-arrangements. a. All patients with adenocarcinoma histology must be tested for EGFR and ALK status, unless a KRAS mutation is detected in which case EGFR/ALK testing is not required. * History of allergy to study drug components or history of severe hypersensitivity reaction of any monoclonal antibody. * History of immune-related adverse event wit prior PD-1/PD-L1 therapy that required discontinuation of treatment * History of (non-infectious) pneumonitis that required steroids, or current pneumonitis. * Any systemic anti-cancer therapy within 3 weeks prior to C1D1 of study therapy, with the following exception: a. Any prior investigational anti-cancer therapy is not permitted within 4 weeks of C1D1. * Ongoing adverse event from previously administered systemic anti-cancer therapy unless has recovered to ≤ grade 1 or at baseline prior to C1D1. a. Subjects with any grade alopecia or ≤ Grade 2 neuropathy are an exception to this criterion and may qualify for the study. * Patients who have not previously been treated with platinum-based based doublet chemotherapy and who, in the judgment of the investigator, have rapidly progressive disease such that serious complications may arise from disease progression within the next 12 weeks will be excluded. * Non-CNS radiotherapy within 1 week prior to C1D1 of study therapy * Active infection requiring systemic therapy * Known history of previous clinical diagnosis of tuberculosis. * Prior or current systemic immunosuppressive therapy (\> 10 mg/day prednisone equivalents) within 7 days prior to C1D1 of study therapy. Inhaled, ocular, intra-articular, intranasal, and topical corticosteroids are permitted in absence of active autoimmune disease. a. Adrenal replacement doses are permitted in the absence of active autoimmune disease. * Has diagnosis of immunodeficiency * History of allogeneic organ transplant. * Patients with known or suspected history of autoimmune disease. a. Subjects with type I diabetes mellitus, hypothyroidism only requiring hormone replacement, resolved childhood asthma/atopy, patients with asthma requiring intermittent bronchodilator therapy, skin disorders (such as vitiligo, psoriasis, or alopecia) not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll. i. Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. * Other active malignancy that is progressing, requires concurrent intervention, and/or could be mistaken for the malignancy under study during disease assessments. * Patients with previous malignancies (except non-melanoma skin cancers, and the following in situ cancers: bladder, gastric, colon, cervical/dysplasia, melanoma, or breast) are excluded unless definitive therapy has been completed at least 1 year prior to study entry and the patient is now without evidence of disease from that malignancy and no additional therapy is required or anticipated to be required during the study period. * Known untreated brain or leptomeningeal metastasis. a. Patients with brain metastases are eligible if metastases have been adequately treated and neurologically returned to baseline (except for residual signs or symptoms related to the CNS treatment) for at least two weeks prior to C1D1 and meet requirements related to steroids noted in above Exclusions Criteria 6.2.10. * History of stroke or transient ischemic attack within the previous 6 months. * Any of the following cardiac abnormalities: 1. Unstable angina pectoris 2. Congestive heart failure ≥ NYHA Class 3 3. QTc ≥470 milliseconds calculated using Frediricia's Correction 4. Current or history of pericardial effusion causing hemodynamic compromise * Patients with a \>/= small pericardial effusion at baseline will be excluded. Patients with \< small pericardial effusion at baseline can continue to proceed onto treatment if other eligibility criteria are met * History of interstitial lung disease (ILD), drug-induced ILD, radiation pneumonitis which required steroid treatment, or any evidence of clinically active interstitial lung disease. * Any positive test for HIV 1/2 antibodies and/or RNA. * Any positive test for hepatitis B virus(HBV) using HBV surface antigen (HBV sAG) test or positive test for hepatitis C virus (HCV) using HCV ribonucleic acid (RNA) or HCV antibody test indicating acute or chronic infection. * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment. * Has received a live vaccine within 30 days of planned start of study therapy. a. Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed.