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

Assessment of Safety and Recommended Phase 2 Dose of Autologous T Cells Engineered With an Affinity-enhanced TCR Targeting NYESO1 and LAGE1a, and Co-expressing CD8α (GSK3901961) in Participants With NYESO1 and/or LAGE1a Positive Previously Treated Advanced (Metastatic or Unresectable) Synovial Sarcoma / Myxoid/Round Cell Liposarcoma; or NYESO1 and/or LAGE1a Positive Previously Treated Metastatic Non-Small Cell Lung Cancer

The primary purpose of this sub study is to assess the safety, tolerability and determine recommended Phase 2 dose (RP2D) of GSK3901961 in HLA A*02:01, HLA-A*02:05 and/or HLA A*02:06 positive participants with New York esophageal squamous cell carcinoma (NY ESO 1) and/or Cancer testis antigen 2 (LAGE 1a) positive previously treated metastatic Non-Small Cell Lung Cancer (NSCLC) and previously treated, advanced (metastatic or unresectable) Synovial Sarcoma/ Myxoid/Round Cell Liposarcoma SS/MRCLS.

This study is a substudy of the Master record - (209012) NCT04526509.

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