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 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 meeting any of the following criteria: a. >=50 Gray (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 patients to prolonged cytopenia after
             lymphodepletion. b. Radiotherapy to the target lesions within 3 months before
             lymphodepletion. A lesion with unequivocal progression may be considered a target
             lesion regardless of time from last radiotherapy dose.

          -  Other protocol-defined inclusion/exclusion criteria may apply.