Study of GSK3901961 In Previously Treated Advanced (Metastatic OR Unresectable) Synovial Sarcoma/ Myxoid/Round Cell Liposarcoma, and Previously Treated Metastatic Non-Small Cell Lung Cancer

Inclusion Criteria: * Participant must be \>=18 years of age and weighs ≥40 kg on the day of signing informed consent * Participant must be positive for HLA-A\*02:01, HLA-A\*02:05, and/or HLA-A\*02:06 alleles * Participant's tumor must have tested positive for NY-ESO-1 and/or LAGE-1a expression by a GSK designated laboratory * Performance status: Eastern Cooperative Oncology Group of 0-1 * Participant must have adequate organ function and blood cell counts 7 days prior to leukapheresis * Participant must have measurable disease according to RECIST v1.1. * Participant has advanced (metastatic or unresectable) SS or MRCLS confirmed by local histopathology with evidence of disease-specific translocation * Participant has completed at least one standard of care (SOC) treatment including anthracycline containing regimen unless intolerant to or ineligible to receive the therapy. * Participants who are not candidates to receive anthracycline should have received ifosfamide unless also intolerant to or ineligible to receive ifosfamide. Participants who received neoadjuvant/adjuvant anthracycline or ifosfamide based therapy and progressed will be eligible * Participant has histologically or cytologically confirmed Stage IV NSCLC * Participant has been previously treated with SOC for Stage IV NSCLC Exclusion Criteria: * Central nervous system (CNS) metastases, with certain exceptions for CNS metastases in NSCLC as specified in the protocol * Any other prior malignancy that is not in complete remission * Clinically significant systemic illness * Prior or active demyelinating disease * History of chronic or recurrent (within the last year prior to leukapheresis) severe autoimmune or immune mediated disease requiring steroids or other immunosuppressive treatments * Previous treatment with genetically engineered NY-ESO-1-specific T cells, NY-ESO-1 vaccine or NY-ESO-1 targeting antibody * Prior gene therapy using an integrating vector * Previous allogeneic hematopoietic stem cell transplant within the last 5 years or solid organ transplant * Washout periods for prior radiotherapy and systemic chemotherapy must be followed * Major surgery within 4 weeks prior to lymphodepletion * Pregnant or breastfeeding females