Pembrolizumab After ASCT for Hodgkin Lymphoma, DLBCL and T-NHL

Inclusion criteria • Histologically confirmed diagnosis with review of the diagnostic pathology specimen at one of the participating institutions. Eligible histologies are: Arm A: Diffuse large B cell lymphoma; patients with a prior history of indolent B-cell NHL are eligible, as long as they have histologically confirmed DLBCL prior to their pre-transplant salvage treatment. Patients with mediastinal large B cell lymphoma are also eligible. Arm B: Classical Hodgkin lymphoma (patients with nodular lymphocyte predominant Hodgkin lymphoma \[NLPHL\] are NOT eligible) Arm C: Peripheral T cell lymphoma - eligible subtypes will include PTCL, NOS; AITL; and ALK-negative ALCL. Patients with other PTCL histologies, including ALK-positive PTCL, and cutaneous T-cell lymphoma will not be eligible.. * Age ≥ 18 at the time of enrollment. * For arms A and B, participants must have relapsed after or been refractory to first-line chemotherapy, i.e., they must have failed to achieve CR after first-line therapy or must have relapsed subsequently if they achieved CR. For arm C, participants will be eligible if transplant is performed as consolidation of first remission (partial or complete). * Participants must be planning to receive or have received autologous stem cell transplantation. Participants must have chemosensitive disease prior to ASCT, defined as achieving at least a partial remission (as determined with PET imaging) to salvage treatment. Participants with cHL or DLBCL (arms A and B) transplanted in 1st remission after only one line of treatment are not eligible. Participants with PTCL (arm C) transplanted beyond 1st remission are also not eligible. * No more than 1 line of anthracycline-containing chemotherapy prior to ASCT, and no more than 3 lines of therapy total prior to ASCT for arms A and B; no more than 1 line of therapy prior to ASCT for arm C. * Participants cannot have received any anti-neoplastic therapy (including radiotherapy, chemotherapy or immunotherapy) after ASCT * Participants must have had PET-CT for restaging after salvage therapy and before ASCT. * Participants must begin study treatment no later than 21 days from the post-ASCT discharge. Additionally, they must have recovered from ASCT toxicities at the time of first study treatment. * ECOG performance status ≤2 * Participants must have normal organ and marrow function as defined below: * absolute neutrophil count ≥ 1,000/mcL * platelets ≥ 50,000/mcL * Hemoglobin ≥ 8 g/dl * total bilirubin ≤ 1.5 × institutional upper limit of normal (ULN), or direct bilirubin ≤ ULN in patients with Gilbert's syndrome * AST(SGOT)/ALT(SGPT) ≤ 2.5 × ULN * Creatinine ≤ 1.5 × ULN or creatinine clearance ≥ 60 mL/min/1.73 m2 * Resting and ambulatory oxygen saturation ≥ 94% on room air * FEV1 and DLCO (adjusted for Hemoglobin) ≥ 50% predicted * Willigness to use contraception * Ability to understand and the willingness to sign a written informed consent document. Exclusion criteria * Participants who are receiving any other investigational agents after ASCT. * Participants with active CNS involvement are excluded. * History of or active autoimmune disease, or other syndrome that requires systemic steroids or autoimmune agents. Participants with vitiligo, resolved childhood asthma or atopy, hypothyroidism, or Sjogren's syndrome, as well as participants requiring only intranasal steroids, intermittent use of bronchodilators, local steroid injections, or physiologic replacement doses of prednisone (≤ 10 mg/d) are not excluded from this study. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to pembrolizumab. Prior hypersensitivity reactions to anti-CD20 therapy or anti-CD30 therapy is not an exclusion criterion. * Has a history of (non-infectious) pneumonitis that required steroids or current pneumonitis. * Receipt of \> 600 mg/m2 total dose of BCNU with prior treatments including transplant conditioning regimen. * Uncontrolled illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements or pose excess risk to the participant in the opinion of the treating clinician.. * Pregnant or lactating women. * HIV-positive. * Participants with active viral hepatitis (positive HepB sAg, positive HepB core Ab with positive HepB viral load, or positive HepC antibody with positive HepC viral load). * Receipt of a live vaccine within 30 days of the start of treatment. Examples are measles, mumps, rubella, varicella, yellow fever, rabies, BCG, oral polio vaccine, and oral typhoid vaccine. * Prior treatment with an anti PD-1, anti PD-L1, or anti CTLA-4 agent. Participants who entered clinical remission with one of those agents and proceeded to ASCT without intervening relapse may be eligible after discussion with the Study Chair. Note that for patients who enter remission with checkpoint blockade therapy, this will not count towards the 3 lines of prior therapy.