Pilot Immunotherapy Study With Letetresgene Autoleucel (Lete-cel, GSK3377794)T-cells in New York Esophageal Squamous Cell Carcinoma-1 (NY-ESO-1)/ LAGE-1a-positive Advanced Non-small Cell Lung Cancer (NSCLC) Either Alone or in Combination With Pembrolizumab

Inclusion Criteria: * Age \>=18 years on the day of signing informed consent. * Histologically or cytologically diagnosed unresectable Stage IIIb or Stage IV NSCLC. * Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1. * Participant is positive for any of the following alleles: human leukocyte antigen (HLA)-A\*02:01, HLA-A\*02:05, and a) or HLA-A\*02:06 by a validated test. * Participant's tumor meets the pre-defined threshold for expression of NY-ESO-1 and/or LAGE-1a. * Adequate organ function and blood cell counts, as defined in the protocol. * Predicted life expectancy that is \>=24 weeks from leukapheresis. * Left ventricular ejection fraction \>=45%. * Prior therapies prior to lymphodepletion: a) All participants with NSCLC lacking actionable genetic aberrations, per National Comprehensive Cancer Network (NCCN) guidelines (Arms A and B), need to have received at least one line of programmed death protein 1/programmed death protein 1 ligand (PD-1/PD-L1) checkpoint blockade therapy. For participants in the metastatic setting, PD-1/PD-L1 checkpoint blockade therapy must have been received either alone, in combination or sequentially with platinum-containing chemotherapy. OR b) All participants with NSCLC with actionable genetic aberrations, per NCCN guidelines (Arm C only), should have received appropriate targeted therapy following NCCN or equivalent country-level guidelines. * Disease progression at time of treatment, as defined in the protocol. * Measurable disease at time of treatment per response evaluation criteria in solid tumors (RECIST) version 1.1 as assessed by local site investigator/radiology. Exclusion Criteria: * Prior treatment: Previous treatment with genetically engineered NY-ESO-1-specific T-cells. Previous NY-ESO-1 vaccine or NY-ESO-1 targeting antibody. Prior gene therapy using an integrating vector. * Prior allogeneic/autologous bone marrow or solid organ transplantation. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to cyclophosphamide, fludarabine, dimethylsulfoxide (DMSO) or other agents used in the study. * Severe hypersensitivity (\>= Grade 3) to pembrolizumab and/or any of its excipients. * Active autoimmune disease that has required systemic treatment in past 2 years. * History of chronic or recurrent (within the last year prior to enrollment) severe autoimmune or active immune-mediated disease requiring steroids or other immunosuppressive treatments. * Uncontrolled intercurrent illness. * Participant has active infection with human immunodeficiency virus (HIV), hepatitis B virus (HBV), hepatitis C virus (HCV), Epstein Barr virus (EBV), cytomegalovirus (CMV), syphilis, or human T lymphotropic virus (HTLV), as defined in protocol. * Known psychiatric or substance abuse disorders. * Symptomatic or untreated central nervous system (CNS) metastases. * Radiotherapy that involves the lung (Percentage of normal lung receiving at least 20 Gray \[Gy\] during radiotherapy \[V20\] exceeding 30% lung volume or mean heart dose \>20 Gy) within 3 months or radiotherapy (including but not limited to palliative radiotherapy) to lung/mediastinum with V20 less than 30% lung volume and with mean heart dose \<=20 Gy within 4 weeks (+/- 3 days). * Radiotherapy of \>=50 Gy to a significant volume of the pelvis, long bones or spine, or a cumulative dose of radiation that, in the investigator's opinion would predispose participants to prolonged cytopenia after lymphodepletion. * All of the participant's measurable lesions have been irradiated within 3 months before lymphodepletion. * Other protocol-defined inclusion/exclusion criteria may apply.