Study to Evaluate Safety and Antitumor Activity of Lete-Cel (GSK3377794) in HLA-A2+ Participants With NY-ESO-1 Positive Previously Treated Advanced (Metastatic or Unresectable) Synovial Sarcoma or Myxoid/Round Cell Liposarcoma

Inclusion Criteria: * Participant must be ≥10 years of age at the time of signing the informed consent. * Participant scheduled to receive clinical drug product supply must also weigh ≥40 kg. * Participant has a diagnosis of synovial sarcoma or myxoid/round cell liposarcoma, confirmed by local histopathology with evidence of disease-specific translocation. * Participant has advanced (metastatic or unresectable) synovial sarcoma or myxoid/round cell liposarcoma. Unresectable refers to a tumor lesion in which clear surgical excision margins cannot be obtained without leading to significant functional compromise. * Male or female. Contraception requirements will apply at the time of leukapharesis and treatment. * Life expectancy ≥24 weeks * Participant has confirmed evidence of a relevant disease-specific translocation per below: * For synovial sarcoma, presence of a translocation involving chromosome 18 (SYT gene) and/or chromosome X (SSX1, SSX2 or SSX4 genes). * For myxoid/round cell liposarcoma, presence of a translocation involving chromosome 12 (DDIT3 gene) and/or chromosome 16 (FUS gene) and/or chromosome 22 (EWSR1 gene). * Participant is either currently being treated with or has completed at least one standard-of-care treatment including anthracycline-containing regimens (e.g., doxorubicin alone, doxorubicin with ifosfamide) for advanced (metastatic or inoperable) disease. Participants who are intolerant to anthracycline may receive ifosfamide alone unless intolerant to or ineligible to receive ifosfamide. Participants who received anthracycline-based therapy in the neoadjuvant/adjuvant setting and progressed will be eligible. * Participant must be positive for HLA-A\*02:01, HLA-A\*02:05, and/or HLA-A\*02:06 alleles by a validated test in a designated central lab prior to leukapheresis * Participant's tumor has been pathologically reviewed by a designated central laboratory with confirmed positive NY-ESO-1 expression defined as ≥30% of cells that are 2+ or 3+ by immunohistochemistry. * Left ventricular ejection fraction ≥45% with no evidence of clinically significant pericardial effusion. * Performance status: for participants \<16 years of age, Lansky \>60, or for participants ≥16 and \<18 years of age, Karnofsky \>60, or for participants ≥18 years of age, Eastern Cooperative Oncology Group (ECOG) of 0-1. * Participant must have adequate organ function and blood cell counts, within 7 days prior to the day of the leukapheresis procedure * Participant is fit for leukapheresis and has adequate venous access for the cell collection * Female participants of childbearing potential (FCBP) must have a negative urine or serum pregnancy test. * Participant has measurable disease according to RECIST v1.1. * Participant has documented radiographic evidence of disease progression from prior line of therapy. * A biopsy (excisional, incisional, or core) of non-target tumor tissue obtained within 28 days prior to initiating lymphodepleting chemotherapy is mandatory if clinically feasible. This biopsy will be used as baseline for biomarker analyses. If it is not feasible to obtain a fresh biopsy, an archival tumor tissue (FFPE block) taken preferably after completion of the participant's last line of therapy, preferably within 90 days prior to initiating lymphodepleting chemotherapy, may be accepted. * A haematologist has been consulted prior to lymphodepletion in participants who have had a serious/significant bleeding/thrombosis history. Exclusion Criteria: * Central nervous system (CNS) metastases. * Any other prior malignancy that is not in complete remission. * 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 * Previous allogeneic hematopoietic stem cell transplant * Clinically significant systemic illness (serious active infections or significant cardiac, pulmonary, hepatic, or other organ dysfunction, that in the judgment of the Investigator would compromise the participant's ability to tolerate protocol therapy or significantly increase the risk of complications) or prior or active demyelinating disease * Participant has received cytotoxic therapy within 3 weeks prior to lymphodepleting chemotherapy * Systemic corticosteroids or any other immunosuppressive therapy within 2 weeks prior to lymphodepleting chemotherapy. * Participant has received ≥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 patients to prolonged cytopenia after lymphodepletion. * All of the participant's measurable lesions have been irradiated within 3 months prior to lymphodepletion. An irradiated measurable lesion with unequivocal progression following irradiation may be considered a target lesion regardless of time from last radiotherapy dose. * Participant has received an anti-cancer vaccine within 2 months in the absence of tumor response. The participant should be excluded if their disease is responding to an experimental vaccine given within 6 months. * Participant has received live vaccine within 4 weeks prior to lymphodepletion or intends to receive live vaccine during the 3-month period following administration of lete-cel. * Participant has received immune therapy (monoclonal antibody therapy, checkpoint inhibitors) within 4 weeks of lymphodepletion. * Participant had major surgery ≥28 days of first dose of study intervention