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.