New York esophageal squamous cell carcinoma-1 (NY-ESO-1) and LAGE-1a antigens are tumor-associated proteins that have been found in several tumor types. Clinical trials using adoptively transferred T- cells directed against NY-ESO-1/LAGE-1a have shown objective responses. Letetresgene autoleucel (GSK3377794) is the first generation of NY-ESO-1 specific T-cell receptor (TCR) engineered T-cells. This is a multi-arm, open-label study of letetresgene autoleucel (lete-cel, GSK3377794) in Human Leukocyte Antigen (HLA)-A\*02:01, HLA-A\*02:05 and/or HLA-A\*02:06 positive adults whose tumors express NY-ESO-1 and/or LAGE-1a. This study will enroll participants who have unresectable Stage IIIb or Stage IV NSCLC.