Phase I Study of Romidepsin, Gemcitabine, Oxaliplatin, and Dexamethasone in Patients With Relapsed/Refractory Aggressive Lymphomas

Inclusion Criteria: * Able to understand and voluntarily sign an informed consent form * Age ≥ 18 at time of informed consent * Diagnosis of one of the following: * relapsed/refractory peripheral T-cell lymphoma of any subtype including mycosis fungoides and Sézary syndrome of advanced stage (IIB-IVB) \*\*for the expansion cohort:patients must have biopsy-proven T-cell lymphoma and measurable disease. * relapsed/refractory DLBCL (up to 6 DLBCL patients are allowed in the dose-escalation portion of the study) * relapsed/refractory HL Note: extracorporeal photopheresis is NOT considered a systemic therapy for this study. * Transplant eligible (as determined by referring physician) patients who have failed one prior salvage therapy or transplant ineligible (as determined by referring physician) patients who have failed one prior therapy * ECOG performance status of ≤ 2 * Laboratory test results within the following ranges: * Absolute neutrophil count ≥ 1500/mm³ * Platelet count ≥ 100,000/mm³ * Total bilirubin ≤ 1.5 x ULN * AST (SGOT) and ALT (SGPT) ≤ 3 x ULN * Creatinine \< 2 mg/dL * Potassium ≥ 3.3 mmol/L or at/above the lower limit of normal for the performing laboratory * Magnesium ≥ 1.4 mg/dL or at/above the lower limit of normal for the performing laboratory. * Negative serum pregnancy test for women of childbearing potential * Washout time of at least 4 weeks for prior biological, chemotherapeutic, or radiotherapy Exclusion Criteria: * Any serious medical condition, laboratory abnormality, or psychiatric illness that would - in the opinion of the investigator - prevent the subject from signing the informed consent form * Pregnant or lactating women * Any medical condition or laboratory abnormalities, which - in the opinion of the investigator - places the subject at unacceptable risk, or confounds the ability to interpret data if he/she were to participate in the study * Positive CSF cytology during staging, symptomatic leptomeningeal involvement, or parenchymal involvement of brain or spinal cord * Prior allogeneic hematopoietic cell transplant * Prior solid organ transplant * Cirrhotic liver disease from any cause * Known HIV infection * Impaired cardiac function or clinically significant cardiac disease including any of the following: * Congenital long QT syndrome * Screening ECG with QTc interval ≥ 500 milliseconds * Myocardial infarction (MI) or unstable angina ≤ 6 months of C1D1; however, subjects with a history of MI between 6 and 12 months who are asymptomatic and have had a negative cardiac risk assessment (treadmill stress test, nuclear medicine stress test, or stress echocardiogram) since the event would be eligible * Symptomatic coronary artery disease (CAD), e.g., angina Canadian Class II-IV. In any patient in whom there is doubt, the patient should have a stress imaging study and, if abnormal, angiography to define whether or not CAD is present * An ECG recorded at screening showing evidence of cardiac ischemia (ST depression of ≥2 mm, measured from isoelectric line to the ST segment). If in any doubt, the patient should have a stress imaging study and, if abnormal, angiography to define whether or not CAD is present * Other significant ECG abnormalities including 2nd degree atrio-ventricular (AV) block type II, 3rd degree AV block, or bradycardia (defined here as ventricular rate \< 50 bpm); right bundle-branch block + left anterior hemi-block (bifasicular block) * Congestive heart failure (CHF) that meets New York Heart Association (NYHA) Class II to IV definitions (see Appendix 9) and/or ejection fraction \<40% by MUGA scan or \<50% by echocardiogram and/or MRI History or presence of sustained ventricular tachycardia (VT), ventricular fibrillation (VF), torsade de pointes, or cardiac arrest * Hypertrophic cardiomegaly or restrictive cardiomyopathy from prior treatment or other causes * Uncontrolled hypertension, i.e., blood pressure (BP) of ≥160/95; patients who have a history of hypertension controlled by medication must be on a stable dose (for at least one month) and meet all other inclusion criteria * Any cardiac arrhythmia requiring an anti-arrhythmic medication, excluding stable (i.e., at least 30 days from screening) doses of beta-blockers * Concomitant use of drugs that may cause significant QT prolongation and/or torsades de pointes that cannot be discontinued or switched to a different medication prior to treatment * Concomitant use of CYP3A4 inhibitors or inducers unless able to stop medication(s) prior to starting study treatment * Patients who are unwilling to stop the use of herbal remedies while receiving study treatment * Unable to accept blood product transfusions * Men whose sexual partners are women of childbearing potential not using a double method of contraception during the study and 3 months after the end of treatment. One of these methods must be a condom * Concurrent malignancy requiring active therapy \*Patients with localized prostate cancer having undergone surgery or radiation (field confined to ≤ 30% of marrow-bearing bone) at least 30 days prior to study treatment are eligible