Abexinostat and Ibrutinib in Diffuse Large B-cell Lymphoma and Mantle Cell Lymphoma

Inclusion Criteria: * Patient is ≥ 18 years of age at the time of signing Informed Consent * Patient is able and willing to adhere to the study visit schedule and other protocol requirements * Patient has histologically confirmed diagnosis of R/R mantle cell lymphoma or diffuse large B cell lymphoma * Diffuse large B cell lymphoma patients must have received at least 1 prior regimen and received, declined, or is ineligible for autologous or allogeneic stem cell transplant. * Diffuse large B cell lymphoma patients must have non-germinal center subtype disease applying the Hans classification algorithm using immunohistochemistry markers CD10, BCL6, and MUM1 (8). * Mantle cell lymphoma patients must have received at least 1 line of therapy * Allogeneic stem cell transplant recipients be greater than 6 months post transplant, not on immunosuppression for prevention of graft versus host disease for \>3 months and without active graft versus host disease * Autologous stem cell transplant recipients must have adequate bone marrow recovery and are transfusion independent * Patients with transformed DLBCL from an antecedent or simultaneous indolent B-cell Non-Hodgkin lymphoma are permitted. * Patient has at least one measurable lesion (≥ 1.5 cm) according to RECIL * Patient has an Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 * Patient has adequate bone marrow and organ function by: * Absolute neutrophil count (ANC) ≥ 1.0 x 10\^9/L independent of growth factor support * Platelets ≥100 x 10\^9/L independent of transfusion °For patients with documented bone marrow involvement of underlying MCL or DLBCL at time of study enrollment, platelets must be ≥75 x 10\^9/L independent of transfusion * Hemoglobin (Hgb) ≥ 9.0 g/dL °For patients with documented bone marrow involvement of underlying MCL or DLBCL at time of study enrollment, Hgb must be ≥ 8.0 g/dL * International Normalized Ratio (INR) ≤ 1.5 * Creatinine clearance \> 25 mL/min as determined by the Cockcroft-Gault equation or a 24-hour urine collection * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ ULN (or ≤3 x ULN if liver involved with disease Total serum bilirubin ≤ 1.5 ULN unless bilirubin rise is due to Gilbert"s syndrome or of non-hepatic origin * Normal serum potassium level with or without supplementation. * Left Ventricular Ejection Fraction (LVEF) ≥ 50% * Women of childbearing potential and men who are sexually active must be practicing a highly effective method of birth control during and after the study consistent with local regulations regarding the use of birth control methods for subjects participating in clinical trial. For females, these restrictions apply for 30 days month after the last dose of study drug. For males, these restrictions apply for 120 days after the last dose of study drug. Refer to section 9.7 "Reproductive toxicity" for additional details * Women of childbearing potential must have a negative urine pregnancy test at Screening and within 7 days of treatment initiation * Men must agree to not donate sperm during and 12 months after the study. Women should not donate ova/ooctyes for the purposes of * Patient is able to swallow and retain oral medications Exclusion Criteria: * Patients previously treated with ibrutinib or HDAC inhibitor * Patient has a history of non-compliance to medical regimen or inability to grant consent * Patient is concurrently using other approved or investigational antineoplastic agent * Patient has not recovered to Grade 1 or better (except alopecia) from related side effects of any prior antineoplastic therapy * Patient has had major surgery or a wound that has not fully healed within 4 weeks of starting study drugs. * Patients who have had chemotherapy or radiotherapy within 2 weeks prior to entering the study * Patient has evidence of active graft versus host disease (GVHD) * Patient has active central nervous system (CNS) disease or meningeal involvement. * Patient has history of stroke or intracranial hemorrhage ≤ 6 months from starting study drugs. * Patient has impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of study drug (e.g., ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection) * Patient has clinically significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of Screening, or any Class 3 (moderate) or Class 4 (severe) cardiac disease as defined by the New York Heart Association Functional Classification, Left Ventricular Ejection Fraction (LVEF) \<50% as determined by Multiple Gated acquisition (MUGA) scan or echocardiogram (ECHO), unstable angina pectoris, symptomatic pericarditis, QTcF \> 480 msec on the screening ECG (using the QTcF formula), or history of congenital long QT syndrome. * Patient has a concurrent active malignancy. * Malignancies treated with a curative intent with an expected life expectancy ≥ 5 years or a non-competing life expectancy risk are eligible (i.e. adequately treated basal or squamous cell carcinoma, non-melanomatous skin cancer, early stage breast cancer, treated prostate cancer or any other cancer from which the patient has been disease free for ≥ 3 years). * Patient with known history of human immunodeficiency virus (HIV), or any uncontrolled active systemic infection. * Patients with acute viral hepatitis or a history of chronic or active HBV or HCV infection. * Hepatisis B surface antigen and core antibody testing are required at screening. If Hepatisis B surface antigen is positive then HBV PCR is required and if positive, then patient will be excluded. * Hepatisis C antibody testing is required at screening. If positive, Hepatisis C PCR is required and if positive, pHepatisis C PCR is required and if positive, then patient will be excluded. * Patient has hepatic failure (Child-Pugh Class C) * Patient is currently receiving increasing or chronic treatment (\> 10 days) with corticosteroids or another immunosuppressive agent. Patients requiring chronic therapy with steroids may take no more than 10mg daily of prednisone or equivalent. * Patient requires chronic treatment with a strong cytochrome P450 (CYP) 3A4 inhibitors, and inducers, or drugs known to induce Torsades de Pointes and the treatment cannot be discontinued or switched to a different medication prior to starting study drug (Appendix 1 and 3). * Patients with known bleeding diathesis (e.g. von Willebrand "s disease) or hemophilia * Patient is currently receiving warfarin or other Vitamin K antagonist. Therapy with heparin, low molecular weight heparin (LMWH), or fondaparinux is allowed. Refer to Section 9.5 for Concomitant medication * Vaccinated with live, attenuated vaccines within 4 weeks of randomization * Patients with any life-threatening illness, medical condition or organ system dysfunction that in the opinion of the investigator could compromise the subject"s safety, interfere with absorption of metabolism of study drugs or put the study outcomes at undue risk. * Women who are pregnant or breastfeeding.