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