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

Background: Over 230,000 new lung cancer cases are diagnosed every year in the United States (U.S.) About 80% of lung cancers are non- small cell lung cancer (NSCLC). Most people have a more advanced stage of the disease that doesn't respond well to standard treatment. Researchers want to see if a combination of drugs may be able to help. Objective: To find out if LMB-100 followed by pembrolizumab can help tumors to shrink in people with NSCLC. Eligibility: People ages 18 and older with NSCLC that has not responded to standard therapies Design: Participants will be screened with: * Medical history * Physical exam * Tumor sample. If one is not available, they will have a biopsy. * Assessments of ability to perform normal activities * Lung function tests * Blood, heart, and urine tests * Computed tomography (CT) and positron emission tomography (PET). They will lie in a machine that takes pictures of the body. Participants will take LMB-100 in 21-day cycles for up to 2 cycles. They will take the drug by injection into an arm vein on days 1, 3, and 5 of each cycle. They will stay in the hospital 7-10 days each cycle. Then they will get pembrolizumab by injection into an arm vein every 3 weeks for up to 2 years. They may be able to take pembrolizumab an additional year if their cancer gets worse. Participants will have repeats of the screening tests throughout the study. About 30 days and 90 days after they stop treatment, participants will have follow-up visits. Then they will have visits every 6-12 weeks. They will be followed for the rest of their life through phone calls and emails.

Background: * Mesothelin is expressed in approximately half of all lung adenocarcinomas. * LMB-100 has demonstrated anti-tumor efficacy against several mesothelin expressing tumor models including non-small cell lung cancer (NSCLC). Programmed death ligand 1 (PD-1) is an Ig superfamily member related to cluster of differentiation (CD28) and cluster of differentiation 152 (CTLA-4) that has been shown to negatively regulate antigen receptor signaling upon engagement of its ligands. * Pembrolizumab, an immunoglobulin G4 (IgG4) monoclonal antagonist antibody to PD-1, is Food and Drug Administration (FDA) approved in the frontline for advanced non-squamous NSCLC as a single agent with high programmed death-ligand 1 (PD-L1) expression \[tumor proportion score (TPS) \>=50%\] or in combination with platinum-based doublet chemotherapy (PD-L1 unselected). It also approved in the second-line for high PDL1 expressing tumors (TPS \>=1%). * Combination treatment with LMB-100 plus pembrolizumab results in greater anti-tumor efficacy in murine lung cancer model. Objectives: -To determine the objective response rate of LMB-100 followed by pembrolizumab in the treatment of subjects with mesothelin-expressing non-squamous non-small cell lung cancer (NSCLC) previously treated with immune checkpoint inhibitors. Eligibility: * Histologically confirmed locally advanced or metastatic non-squamous, non-small cell lung cancer lacking an EGFR sensitizing mutation, anaplastic lymphoma kinase (ALK) or ROS oncogene 1 (ROS1) gene rearrangement and not amenable to potentially curative surgical resection or chemoradiation. * Tumor mesothelin expression of at least 25% of tumor cells as determined by the Laboratory of Pathology at the NCI. * Subjects must have at least progressed after one prior platinum-based doublet chemotherapy AND standard immune checkpoint inhibitor (ICI) with either frontline single-agent pembrolizumab, or in combination with platinum-based doublet chemotherapy, or second-line single-agent nivolumab, pembrolizumab, or atezolizumab. * Age \>= 18 years. Design: * This is an open-label, single center phase II study of LMB-100 followed by pembrolizumab in subjects with mesothelin expressing NSCLC who have progressed on standard therapies * Subjects will receive LMB-100 at the single agent maximum tolerated dose (MTD) (140mg/kg) on days 1, 3 and 5 of a 21-day cycle for up to 2 cycles and pembrolizumab 200 mg on day 1 of cycle 3 of a 21- day cycle (or cycle 2 if disease progression is observed after 1 cycle) onwards until disease progression (on or after pembrolizumab) or intolerable toxicity for a maximum of 2 years (unless second course initiated). * The total accrual ceiling for the screening will be set at 100 total patients in order to treat 23 subjects.