Phase II Study of Second- Line Pembrolizumab Plus GVD for Relapsed or Refractory Hodgkin Lymphoma

Inclusion Criteria: * Histologic diagnosis of classical Hodgkin's lymphoma. Primary refractory or relapsed disease proven by biopsy at enrolling institution. * Stage I-III Hodgkin lymphoma (part 3) * Relapse or refractory disease following 1 line of multi-agent chemotherapy (not including pembro-GVD). * Eligible for HDT/ASCT * Achieved complete response (Deauville 3 or better) per clinical review following 2 cycles of pembro-GVD * Be willing and able to provide written informed consent/assent for the trial. * Be ≥ 18 years of age on day of signing informed consent. * Have measurable disease based on Lugano 2014 criteria * Have a performance status of 0 or 1 on the ECOG Performance Scale * Demonstrate adequate organ function as defined in table below * Demonstrate adequate organ function as defined in table below. Hematological\* * Absolute neutrophil count (ANC) ≥1000 /mcL * Platelets ≥50,000 / mcL * Hemoglobin ≥8 g/dL Renal * Serum creatinine OR ≤1.5 X upper limit of normal (ULN) OR * Measured or calculated creatinine clearance (eGFR can also be used in place of creatinine) ≥60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN Hepatic\* * Serum total bilirubin ≤ 1.5 X ULN OR ≤ 3 X ULN for subjects with liver metastases * AST (SGOT) and ALT (SGPT) ≤ 2.5 X ULN OR ≤ 5 X ULN for subjects with liver metastases Pulmonary * Hemoglobin-adjusted diffusing capacity for carbon monoxide ≥50% (If unadjusted DLCO is \>/= 50% then there is no need to calculate adjusted) Cardiac * Ejection fraction ≥45% Coagulation * International normalized ratio (INR) OR prothrombin time (PT), Activated partial thromboplastin time (aPTT): ≤ 1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants \*Lab values for eligibility should be based upon labs prior to Cycle 1 treatment of Pembro-GVD. * Female subject of childbearing potential should have a negative urine or serum pregnancy within 2 weeks prior to receiving the first dose of study medication. On the day of planned treatment, if a blood pregnancy test has not been performed within the two week window, a stat pregnancy test (urine or blood) should be performed and the results reviewed before treatment is begun. * Female subjects of childbearing potential must be willing to use an adequate method of contraception (see details in section 11.4.3). * Male subjects of childbearing potential must agree to use an adequate method of contraception.(see details in section 11.4.3). * HIV-infected participants must have well-controlled HIV on ART, defined as: * Participants on ART must have a CD4+ T-cell count ≥350 cells/mm3 at the time of screening * Participants on ART must have achieved and maintained virologic suppression defined as confirmed HIV RNA level below 50 copies/mL or the LLOQ (below the limit of detection) using the locally available assay at the time of screening and for at least 12 weeks before screening * It is advised that participants must not have had any AIDS-defining opportunistic infections within the past 12 months. * Participants on ART must have been on a stable regimen, without changes in drugs or dose modification, for at least 4 weeks before study entry (Day 1) and agree to continue ART throughout the study * Participants who have AEs due to previous anticancer therapies must have recovered to ≤Grade 1 or baseline. Participants with endocrine-related AEs who are adequately treated with hormone replacement or participants who have ≤Grade 2 neuropathy are eligible. Exclusion Criteria: * Received more than 1 prior treatment (combined modality therapy represents 1 treatment) for Hodgkin Lymphoma * Known pregnancy or breast-feeding. * Breast-feeding should be discontinued prior to treatment initiation. * Medical illness unrelated to Hodgkin's Lymphoma, which, in the opinion of the attending physician and/or principal investigator, makes participation in this study inappropriate. * Has received prior radiotherapy within 2 weeks of start of study treatment. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. * Has known active HIV, Hepatitis B (e.g., Hepatitis B PCR positive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). * Has received a live vaccine or live-attenuated vaccine within 30 days prior to the first dose of study drug. Administration of killed vaccines is allowed. * Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. * Has an active infection requiring systemic therapy. * Has not adequately recovered from major surgery or has ongoing surgical complications * Has undergone solid organ transplant at any time, or prior allogeneic hematopoietic stem cell transplantation within the last 5 years. (Subjects who have had an allogeneic hematopoietic transplant greater than 5 years ago are eligible as long as there are no symptoms of GVHD.) * Has a history or current evidence of any condition, therapy, or laboratory abnormality or other circumstance that might confound the results of the study, interfere with the participant's participation for the full duration of the study, such that it is not in the best interest of the participant to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.