Pembrolizumab and Pralatrexate in Treating Patients With Relapsed or Refractory Peripheral T-Cell Lymphomas

Inclusion Criteria: * Documented willingness and ability to sign an informed consent of the participant and/or legally authorized representative. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Patients must have a histologically confirmed diagnosis of mature peripheral T-cell or natural killer (NK)-cell lymphoma according to the World Health Organization (WHO) classification, with hematopathology review at the participating institution. Eligible histologies are: * Peripheral T-cell lymphoma, not otherwise specified * Anaplastic large cell lymphoma, ALK-negative * Anaplastic large cell lymphoma, ALK-positive * Angioimmunoblastic T-cell lymphoma * Nodal peripheral T-cell lymphoma with TFH phenotype * Follicular T-cell lymphoma * Indolent T-cell lymphoproliferative disorder of the gastrointestinal (GI) tract * Extranodal NK-/T-cell lymphoma * Enteropathy-associated T cell lymphoma * Monomorphic epitheliotropic intestinal T-cell lymphoma * Hepatosplenic T-cell lymphoma * Subcutaneous panniculitis-like T-cell lymphoma * Transformed mycosis fungoides * Patients must have failed at least one prior regimen, including: * Recurrence of disease after a documented complete response (CR). * Progression of disease after a partial response (PR) to the prior regimen. * Partial response, stable disease (SD) or progressive disease (PD) at the completion of the prior treatment regimen. If a patient has PR to prior regimen without P…