Romidepsin in Combination With Lenalidomide in Adults With Relapsed or Refractory Lymphomas and Myeloma

Inclusion Criteria: * Pathology confirmed lymphoma or multiple myeloma * Hodgkin lymphoma is eligible for either phase and will be considered a B-cell lymphoma in the phase IIa study. * Phase IIa portion, subjects must have B-cell lymphoma, T-cell lymphoma, or multiple myeloma. * Relapse or progression after at least 1 systemic therapy. * Measurable disease for phase IIa portion only. * Lymphoma (includes CTCL patients who are NED in skin): CT or PET/CT by modified Cheson criteria with incorporation of PET. * Multiple myeloma:.Patient must have measurable disease and therefore must have at least one of the following: i. Serum M-protein ≥0.5gm/dL (≥5gm/L) ii. Urine M-protein ≥200mg/24hr iii. Serum FLC assay: involved FLC ≥10mg/dL (≥100mg/L) provided serum FLC ratio is abnormal. * CTCL: mSWAT \>0, or absolute Sezary count ≥ 1000 cells/μL. * Age ≥18 years at the time of signing the informed consent form. * Able to adhere to the study visit schedule and other protocol requirements. * Previous systemic anti-cancer therapy must have been discontinued at least 3 weeks prior to treatment in this study. If there is progression of disease on that therapy and all adverse effects have resolved to Grade 1 or baseline, in which case 2 weeks is acceptable. * Previous radiation, hormonal therapy, and surgery must have been discontinued or completed at least 2 weeks prior to treatment in this study and adverse effects must have resolved. Lymph node or other diagnostic biopsy within 2 weeks is not considered exclusionary. * Short course systemic corticosteroids for disease control, improvement of performance status or non-cancer indication (\< 7 days) must have been discontinued at least 7 days prior to study treatment. Stable ongoing corticosteroid use (≥ 30 days) up to an equivalent dose of 15 mg of prednisone is permissible. * ECOG performance status of ≤ 2 at study entry * Laboratory test results within these ranges: * Absolute neutrophil count ≥ 1.0/mm³. * Platelet count ≥ 70 K/μL, if thrombocytopenia is due to bone marrow involvement platelet count must be ≥ 50 K/μL. * Renal function assessed by calculated creatinine clearance as follows * Phase Ib subjects must have calculated creatinine clearance ≥ 50ml/min by Cockcroft-Gault formula. * Phase IIa subjects must have calculated creatinine clearance ≥ 30ml/min by Cockcroft-Gault formula. See section below, "Dosing Regimen", regarding lenalidomide dose adjustment for calculated creatinine clearance \< 60ml/min and ≥ 30ml/min. * Total bilirubin ≤ 1.5 x upper limit of normal (ULN); 3 x ULN if due to hepatic involvement. * AST (SGOT) and ALT (SGPT) ≤ 3 x ULN; 5 x ULN if due to hepatic involvement. * All study participants must be registered into the mandatory Revlimid REMS® program, and be willing and able to comply with the requirements of the REMS® program. * Females of reproductive potential must adhere to the scheduled pregnancy testing as required in the Revlimid REMS® program. Men must agree to use a latex condom during sexual contact with a FCBP even if they have had a successful vasectomy. See Appendix C: Risks of Fetal Exposure, Pregnancy Testing Guidelines and Acceptable Birth Control Methods. † A female of childbearing potential is a sexually mature female who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months). Exclusion Criteria: * Patients who have a standard curative option for their lymphoid malignancy at current state of disease are excluded. For eligibility on this trial, allogeneic stem cell transplantation is not to be considered a standard curative option. * Any serious medical condition, laboratory abnormality, or psychiatric illness that would prevent the subject from signing the informed consent form. Pregnant females. (Lactating females must agree not to breast feed while taking lenalidomide or romidepsin). * Known hypersensitivity to thalidomide. * The development of erythema nodosum if characterized by a desquamating rash while taking thalidomide or similar drugs. * Prior use of lenalidomide if discontinued due to toxicity. * Prior therapy with romidepsin if discontinued due to toxicity. * Concurrent use of other anti-cancer agents or treatments. * Known seropositive and requiring anti-viral therapy for human immunodeficiency virus (HIV), hepatitis B virus (HBV) or hepatitis C virus (HCV). * Active concurrent malignancy requiring active therapy. * Known central nervous system or meningeal involvement (in the absence of symptoms investigation into central nervous system involvement is not required). Patients with HTLV1 ATLL and controlled CNS or meningeal involvement may be enrolled after discussion with the MSK principal investigator. * The following known cardiac abnormalities: * Congenital long QT syndrome. * QTc interval ≥ 480 milliseconds * A QTc interval between 480-499 msec in the presence of a bundle branch block (BBB) or pacemaker is are eligible in phase IIa after discussion with the MSK principal investigator * Myocardial infarction within 6 months of cycle one, day one (C1D1). Subjects with a history of myocardial infarction between 6 and 12 months prior to C1D1 who are asymptomatic and have had a negative cardiac risk assessment (treadmill stress test, nuclear medicine stress test, or stress echocardiogram) since the event may participate. * Other significant ECG abnormalities including 2nd degree atrio-ventricular (AV) block type II, 3rd degree AV block. Symptomatic coronary artery disease (CAD), e.g., angina Canadian Class II-IV (see Appendix D). 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. * Congestive heart failure (CHF) that meets New York Heart Association (NYHA) Class II to IV definitions (see Appendix E) and/or ejection fraction \<45% by MUGA, echocardiogram, or cardiac MRI. * A known history of sustained ventricular tachycardia (VT), ventricular fibrillation (VF), Torsade de Pointes, or cardiac arrest unless currently addressed with an automatic implantable cardioverter defibrillator (AICD). Hypertrophic cardiomegaly or restrictive cardiomyopathy from prior treatment or other causes. * Uncontrolled hypertension, i.e., blood pressure (BP) of ≥170/95; 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 doses of beta-blockers) * Patients taking drugs leading to significant QTc prolongation unless able to be switched to non-QTc prolonging medication without risk of worsening underlying condition and meet all other inclusion criteria: Medications That May Cause QTc Prolongation). * Concomitant use of significant CYP3A4 inhibitors unless able to be switched to a non-CYP3A4 inhibiting medication without risk of worsening underlying condition and able to meet all other inclusion criteria.