A Study to Evaluate the Safety, Tolerability, Drug Levels, and Preliminary Efficacy of Relatlimab Plus Nivolumab in Pediatric and Young Adults With Hodgkin and Non-Hodgkin Lymphoma

Inclusion Criteria: * Participants with pathologically confirmed high-risk R/R cHL, after non-response to or failure of 1or more lines of standard therapy. * Participants with pathologically confirmed R/R NHL after non-response to or failure of 1or more lines of standard therapy, including, but not limited to, R/R primary mediastinal B-cell lymphoma, diffuse large B-cell lymphoma (DLBCL), mediastinal gray zone lymphoma (MGZL), anaplastic large cell lymphoma (ALCL), or peripheral T-cell lymphoma (PTCL). * Participants with pathologically confirmed R/R NHL after non-response to or failure of 2 or more lines of standard therapy, including Burkitt lymphoma (blast count \<25% malignant Burkitt cells and/or per the investigator's clinical assessment of risk status), lymphoblastic lymphoma (blast count \< 25% of marrow nucleated cells and/or per the investigator's clinical assessment of risk status), NK/T-cell lymphoma (nasal and non-nasal NK/T-cell lymphoma subtypes, but not aggressive NK/T-cell leukemia/lymphoma subtype). * The participant's current disease state must be R/R to standard therapy. * Participants must have measurable PET positive disease in both cHL and NHL cohorts. Exclusion Criteria: * Primary CNS lymphoma of the brain or spinal cord, and secondary CNS lymphoma (ie, from systemic non-Hodgkin lymphoma) involving the brain, spinal cord, or with leptomeningeal seeding. * Prior treatment with an anti-cytotoxic T-lymphocyte-associated protein 4 (anti-CTLA-4) antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways, with the exception of anti-PD(L)-1 targeted therapies. * Prior treatment with lymphocyte activation gene-3 (LAG-3)-targeted agents. * Participants with clinically significant systemic illnesses unrelated to the cancer as judged by the investigators, which would compromise the participant's ability to tolerate the study treatment. * Participants with autoimmune disease. * Prior allogeneic bone marrow transplantation. Other protocol-defined inclusion/exclusion criteria apply