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.