Phase I Dose-finding and Preliminary Efficacy Study of the Istodax® in Combination With Doxil® for the Treatment of Adults With Relapsed or Refractory Cutaneous T-cell Lymphoma

Inclusion Criteria: 1. Able to understand and voluntarily sign an informed consent form. 2. Age ≥18 years at the time of signing the informed consent form. 3. Able to adhere to the study visit schedule and other protocol requirements. 4. Biopsy-proven, measurable, Stage IB-IVB relapsed or refractory cutaneous T-cell lymphoma after 2 lines of skin-directed therapy or one prior line of systemic therapy (Note: extracorporeal photopheresis will be considered a systemic therapy for this study) 5. All cancer therapy, including radiation, hormonal therapy and surgery, must have been discontinued at least 4 weeks prior to treatment in this study. The only exceptions are participants with erythroderma who have been on corticosteroids for prolonged periods of time (\>60 days) without change may continue use of either low dose systemic steroid (equivalent to \<10 mg per day of prednisone) or low potency topical steroids are eligible for this study if the frequency and dosage steroids has not changed for 60 days prior to the study. These participants should continue on the same dose of systemic/topical steroid throughout the study period unless they achieve a complete response at which time steroids can be discontinued. Patients are allowed to continue any medications with known activity in T cell lymphomas at the pre-enrollment doses for conditions other than T cell lymphomas (ie, steroids for sarcoidosis) , as long as there is evidence of T cell lymphoma progression while patients were on these agents. 6. Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2 at study entry. 7. Laboratory test results within these ranges: * Absolute neutrophil count ≥750/mm³ * Platelet count≥75,000/mm³ * Total bilirubin ≤ 2 x upper limit of normal (ULN) * ULN and Aspartate Aminotransferase (ALT) (SGPT) ≤ 3 x ULN. * Creatinine \< 2 mg/dL 8. Disease free of prior malignancies for ≥ 5 years with exception of currently treated basal cell, squamous cell carcinoma of the skin, or carcinoma in situ of the cervix or breast. Patients with early stage of prostate cancer under clinical surveillance without therapy are eligible 9. Negative serum pregnancy test at the time of enrollment for females of childbearing potential. 10. For males and females of child-producing potential, use of effective contraceptive methods during the study to include 2 methods of contraception, one being a condom. 11. Life expectancy \>90 days. Exclusion Criteria: 1. Any serious medical condition, laboratory abnormality, or psychiatric illness that would prevent the subject from signing the informed consent form. 2. Pregnant or breast feeding females. 3. Any condition, including the presence of laboratory abnormalities, which places the subject at unacceptable risk if he/she were to participate in the study or confounds the ability to interpret data from the study. 4. Use of any other experimental drug or therapy within 28 days of baseline except topical therapy for mycosis fungoides which must be discontinued 14 days prior to initiation of study therapy. 5. Prior allogeneic hematopoietic cell transplant. 6. Prior solid organ transplant. 7. Cumulative anthracycline exposure greater than 300 mg/m2 doxorubicin equivalents. 8. Known active viral infection with human immunodeficiency virus (HIV), hepatitis B virus (HBV) or hepatitis C virus (HCV). Patients who are seropositive because of prior hepatitis B virus vaccination are eligible. 9. Central nervous system or meningeal involvement 10. Any known cardiac abnormalities including: * Congenital long QT syndrome * Baseline QTc interval ≥ 480 milliseconds; * Myocardial infarction within 6 months of Cycle 1 Day 1 (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, or bradycardia (ventricular rate less than 50 beats/min) * 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 * Congestive heart failure (CHF) that meets New York Heart Association (NYHA) Class II to IV definitions (see Appendix 10) and/or ejection fraction \<40% by Multigated Acquisition Scan (MUGA) scan or \<50% by echocardiogram and/or 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 ≥160/95; patients with 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) * Any cardiac finding that is deemed ineligible at the discretion of the investigator 11. Patients taking drugs leading to significant QT prolongation and unable to stop drugs prior to treatment 12. Concomitant use of CYP3A4 inhibitors or inducers unless able to stop medication(s) prior to starting study therapies