Combination Therapy With Entinostat and Pembrolizumab in Relapsed and Refractory Lymphomas

Inclusion Criteria: * Patient is ≥ 18 years of age at the time of signing Informed Consent * Patient has histologically confirmed diagnosis of classical Hodgkin lymphoma at enrolling institution. * Hodgkin lymphoma patients must have received at least 2 prior regimens. Patients should have declined, or be ineligible for autologous transplant * Prior HDAC inhibitor and/or anti-PD1, anti-PDL1, anti-PD-L2, anti-CD137 or anti-cytotoxic T- lymphocyte associated antigen 4 (CTLA-4) antibody allowed as long patient received clinical benefit from it. Patients can currently be on a checkpoint inhibitor or HDAC inhibitor, including one of the study drugs, at time of screening. * Patient has at least one site of measurable disease (≥ 1.5 cm), which may be lymph node or extranodal lesion, which is seen on screening imaging studies within 28 days of start of study drug * Patient has an Eastern Cooperative Oncology Group (ECOG) performance status ≤ 1 * Patient has adequate bone marrow and organ function by: * Absolute neutrophil count (ANC) ≥ 1.0 x 10\^9/L * Platelets ≥75 x 10\^9/L * Hemoglobin (Hgb) ≥ 9.0 g/dL * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 1.5 x ULN (or ≤3 x ULN if liver involved with disease * Total serum bilirubin or plasma bilirubin ≤ 1.5 x ULN ( ≤ 3 x ULN with direct bilirubin within normal range in patients with documented hepatic involvement, well documented Gilbert"s Syndrome) * International Normalized Ratio (INR) or Prothrombin * Time (PT) ≤1.5×ULN unless patient is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants * Activated Partial Thromboplastin Time (aPTT) ≤1.5×ULN unless patient is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants * Patients with GFR\>45 ml/min. Patients with GFR 45-59 ml/min are eligible but will undergo dose adjustments as specified in section 9.0.1 * Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * Female subjects of childbearing potential must be willing to use an adequate method of contraception. Subjects must adhere to the contraception requirement from the day of study medication initiation, (or 14 days prior to the initiation of study medication for oral contraception) throughout the entire study, and up 120 days after the last dose of trial therapy. Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. * Male subjects of childbearing potential (Section 9.8.2) must agree to use an adequate method of contraception as outlined in Section 9.8.2- Subjects must adhere to the contraception requirement from the day of study medication initiation, (or 14 days prior to the initiation of study medication for oral contraception) throughout the entire study, and up 120 days after the last dose of trial therapy. Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. Exclusion Criteria: * Diagnosed or treated for malignancy other than the indication under study except for * Malignancy treated with curative intent and with no known active disease present for at least 2 years before the first dose of study treatment * Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease * Adequately treated cervical carcinoma in situ without evidence of disease * History of Human Immunodeficiency Virus (HIV) * Active Hepatitis B or C infection * History of active TB (Bacillus Tuberculosis) * Concurrent enrollment in another therapeutic investigational clinical study or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of study drug * Known CNS lymphoma involvement * Any uncontrolled active systemic infection or any life-threatening illness, medical condition, or organ system dysfunction which, in the investigator"s opinion, could compromise the subject"s safety, interfere with the absorption or metabolism of entinostat capsules, or put the study outcomes at undue risk. * Any history of (non-infectious) pneumonitis that required steroids, evidence of interstitial lung disease or active, non- infectious pneumonitis * Myocardial infarction or arterial thromboembolic events within 6 months prior to baseline or severe or unstable angina, New York Heart Association (NYHA) Class III or IV disease, or a QTc interval \> 470 msec. * History of Torsades de pointes, ventricular tachycardia, or ventricular fibrillation within 6 months prior to screening * Uncontrolled heart failure or hypertension or uncontrolled diabetes mellitus * Any active autoimmune disease or a documented history of autoimmune disease (excluded/exception to the rule: subjects with vitiligo or resolved childhood asthma/atopy, type I diabetes mellitus, subjects with hypothyroidisms stable on hormone replacement, Sjorgen"s syndrome, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger). * Any syndrome that requires ongoing systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 7 days of study drug administration. Of note: Inhaled or topical steroids, and adrenal replacement doses are permitted * Women who are pregnant or breast feeding * Has received a live vaccine or live-attenuated vaccine within 30 days of planned start of study therapy. Administration of killed vaccines is allowed. Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed * Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study Day 1 or has persistent and uncontrolled adverse events from most recent prior therapy. * Patient has had prior allogenic tissue/solid organ transplant \<1 year ago °Participants with prior allo transplant \>1 year ago may enroll if: * Patient does not have active GVHD and has discontinued all GVHD-related medications. * Has received at least 3 doses of PD-1 blockade after allogeneic stem cell transplant without developing acute or chronic GVHD * Patient may enroll after discussion with MSK PI * Has had recent chemotherapy within 2 weeks prior to study day 1 * Has had recent small molecule therapy within 3 half-lives of agent prior to study day 1 °Participants must have recovered from all AEs due to previous therapies to \</= Grade 1 or baseline. Participants with \</= Grade 2 neuropathy may be eligible * Has received radiotherapy (with the exclusion of radiation to one area \[e.g. involved nodal sit\] that does not interfere with response assessment in other sites) within 2 weeks prior to study day 1 °Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis * Allergy to benzamide or inactive components of entinostat