LMB-100 Followed by Pembrolizumab in the Treatment of Adults With Mesothelin-Expressing Non-Squamous Non-Small Cell Lung Cancer (NSCLC)

* INCLUSION CRITERIA: Participants are eligible to be included in the study only if all of the following criteria apply. * Male and female participants who are at least 18 years of age on the day of signing the informed consent will be enrolled in the study. * Subjects must have histologically confirmed diagnosis of non-squamous non-small cell lung cancer not amenable to potentially curative treatments (surgical resection, definitive radiation therapy or a combined modality approach) or targeted agents to actionable epidermal growth factor receptor (EGFR) mutations or Anaplastic lymphoma kinase (ALK) or ROS oncogene 1 (ROS1) gene rearrangement and excluding neuroendocrine tumors. Activating Kirsten rat sarcoma viral oncogene homolog (KRAS) mutations are allowed. The diagnosis must be confirmed by the Laboratory of Pathology, Center for Cancer Research (CCR), National Cancer Institute (NCI). Mutation confirmation may be done by referring institutions or by one of the assays in the Protocol. * Have provided archival tumor tissue sample or newly obtained fresh core or excisional biopsy of a tumor lesion not previously irradiated. Formalin-fixed, paraffin embedded (FFPE) tissue blocks are preferred to slides. Newly obtained biopsies are preferred to archived tissue. * Histologically confirmed 25% of tumor cells expressing mesothelin as determined by NCI Laboratory of Pathology. Determination can be made using archival tumor tissue or fresh biopsy. * Have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST). Lesions in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. * Subjects must have received prior standard of care treatments for locally advanced or metastatic non-small cell lung cancer (NSCLC). * Patients must be more than 3 weeks out of systemic treatments, such as chemotherapy. * All acute toxic effects of any prior radiotherapy, chemotherapy, immunotherapy, or surgical procedure must have resolved to Grade less than or equal to 1, except alopecia (any grade) and Grade 2 peripheral neuropathy. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Evaluation of ECOG is to be performed within 7 days prior to start of study therapy. * Have adequate organ and marrow function as defined below: * Patients must have normal organ and marrow function as defined below: * hemoglobin greater than or equal to 9g/dL or 5.6 mmol/L * absolute neutrophil count greater than or equal to 1,500mcL * platelets greater than or equal to 100,000/mcL * total bilirubin less than or equal to 2.5 x the upper limit of normal range (UNL) OR direct bilirubin less than or equal to ULN for participants with total bilirubin levels of greater than 1.5 X ULN * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) less than or equal to 2.5 x ULN OR less than or equal to 5 x ULN for subjects with metastatic disease to the liver * creatinine greater than or equal to 1.5 x ULN OR creatinine clearance greater than or equal to 50 mL/min for participants with creatinine levels greater than 1.5 X ULN * International normalized ratio (INR) or prothrombin time (PT) or activated thromboplastin time (aPTT) greater than or equal to 1.5 X ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants * Must have left ventricular ejection fraction \>50%. * The effects of LMB-100 on the developing human fetus are unknown. For this reason and because anti-PD-1 antibodies such as pembrolizumab are assumed to be teratogenic: * A male participant must agree to use contraception during the treatment period and for at least 180 days after the last dose of study treatment and refrain from donating sperm * A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies: * Not a woman of childbearing potential (WOCBP) OR * A WOCBP who agrees to follow the contraceptive guidance during the treatment period and for at least 180 days after the last dose of study treatment. * Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. * Ability of subject to understand and the willingness to sign a written informed consent document. * Subjects with non-life-threatening immune-related endocrinopathies or adverse events (AEs) reduced to Grade 1 or 0 after withholding immune checkpoint inhibitors (ICI) or medical intervention are eligible as long as the AE resolved within 12 weeks of last dose and not requiring corticosteroids. EXCULSION CRITERIA: * 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 treatment. Note: Participants 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. * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e., without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to first dose of study treatment. * Subjects who have received prior therapy with LMB-100. Has received prior systemic anti-cancer therapy including investigational agents within 4 weeks prior to start of study therapy. * Note: Participants must have recovered from all AEs due to previous therapies to \<=Grade 1 or baseline. Participants with \<=Grade 2 neuropathy may be eligible. * Note: If participant received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment. * Has received prior radiotherapy within 2 weeks of start of study treatment. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 2-week washout is permitted for palliative radiation (\<=2 weeks of radiotherapy) to non-CNS disease. * Has received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist(R)) are live attenuated vaccines and are not allowed. * Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to start of study therapy. * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). 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. * Has a history of (non-infectious) pneumonitis/interstitial lung disease (ILD) that required steroids or has current pneumonitis/ILD * Has a history or current evidence of any condition, therapy, 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 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. * A WOCBP who has a positive urine pregnancy test within 72 hours prior to start of study therapy. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. Note: In the event that 72 hours have elapsed between the screening pregnancy test and the first dose of study treatment, another pregnancy test (urine or serum) must be performed and must be negative in order for subject to start receiving study medication. * Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 180 days after the last dose of trial treatment. Pregnant women are excluded from this study because LMB-100 + pembrolizumab are agents with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with LMB-100 + pembrolizumab, breastfeeding should be discontinued if the mother is treated with LMB-100 + pembrolizumab. These potential risks may also apply to other agents used in this study. * Has a known history of Human Immunodeficiency Virus (HIV). HIV positive patients will be excluded due to a theoretical concern that the degree of immune suppression associated with the treatment may result in progression of HIV infection. (Note: No HIV testing is required) * Has a known history of Hepatitis B (defined as Hepatitis B surface antigen \[HBsAg\] reactive) or known active Hepatitis C virus (defined as HCV ribonucleic acid (RNA \[qualitative\] is detected) infection. or active hepatitis B virus (HBV) or HCV infection. (Note: No testing for Hepatitis B and Hepatitis C is required.) * Has a known additional malignancy that is progressing or has required active treatment within the past 2 years. Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ (e.g., breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy are not excluded. * Has an active infection requiring systemic therapy. * Participants with contra-indication and/or history of severe hypersensitivity reactions to any components related to LMB-100 or pembrolizumab (or any other immune checkpoint inhibitor such as Programmed death ligand 1 (PD-1), programmed death-ligand 1 (PD-L1) and cluster of differentiation 152 (CTLA-4). * Active or uncontrolled infections. * Subjects who experienced severe or life-threatening immune-related AEs with prior immune checkpoint therapy requiring medical intervention (steroid or immunosuppressant drugs) and permanent discontinuation of therapy, will be excluded. These include, but not limited to colitis, autoimmune hepatitis, hypophysitis, hyperthyroidism, nephritis, myocarditis, Guillain-Barré syndrome (GBS), encephalitis. * Subjects with a history of pneumonitis that required steroids will be excluded. * Recruitment Strategies Information about the study will be posted on sites such as clinicaltrials.gov and the Center for Cancer Research (CCR) recruitment website. Subjects will also be drawn from patients seen at the thoracic clinic at the National Institutes of Health (NIH) Clinical Center as well as from referrals from outside providers. Social media platforms managed by NIH/National Cancer Institute (NCI) may also be used to publicize the study. There is no plan to advertise this study at this time.