Brief Summary: This phase I/II trial studies the side effects and best dose of pralatrexate when given together with pembrolizumab and how well they work in treating patients with peripheral T-cell lymphomas that has come back after a period of improvement or has not responded to treatment. Pralatrexate may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Immunotherapy with monoclonal antibodies, such as pembrolizumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Giving pembrolizumab and pralatrexate may work better in treating patients with peripheral T-cell lymphomas.

Detailed Description: PRIMARY OBJECTIVES: I. Evaluate the safety and tolerability of a regimen combining pembrolizumab and pralatrexate in patients with relapsed or refractory peripheral T-cell lymphoma (PTCL). II. Establish the maximum tolerated dose (MTD) and recommended phase II dose (RP2D) of the combined pralatrexate and pembrolizumab regimen. III. Estimate the overall response rate (ORR) according to the Lugano Classification in patients treated with pembrolizumab plus pralatrexate at the RP2D. SECONDARY OBJECTIVES: I. Estimate the complete response (CR) rate according to the Lugano Classification duration of response (DOR), overall survival (OS) and progression-free survival (PFS) in patients treated with pembrolizumab plus pralatrexate. II. Estimate the ORR and CR rate according to the International Harmonization Project response criteria. III. Evaluate responses and disease progression according to the Lymphoma Response to Immunomodulatory therapy Criteria (LYRIC). EXPLORATORY OBJECTIVE: I. Explore immunologic and genomic biomarkers of response to pembrolizumab plus pralatrexate therapy. OUTLINE: This is a phase I, dose-escalation study of pralatrexate followed by a phase II study. Patients receive pralatrexate intravenously (IV) over 3-5 minutes on days 1 and 8 and pembrolizumab IV over 30 minutes on day 1. Courses repeat every 21 days for up to 24 months in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up at 30 and 90 days, every 12 weeks for 1 year, and then every 18 weeks thereafter.