Romidepsin, Gemcitabine, Dexamethasone and Cisplatin in the Treatment of Peripheral T-Cell and Diffuse Large B-Cell Lymphoma

Inclusion Criteria: * Patients with histologically confirmed PTCL. Biopsy proof of disease at initial diagnosis is mandatory. A biopsy at relapse is preferred but not mandatory. * Patients must have received one or two previous regimens of therapy for their disease (salvage chemotherapy plus autologous stem cell transplantation is considered to be one regimen). * Clinically and / or radiologically measurable disease (1 site bidimensionally measurable). Measurements / evaluations must be done within 28 days prior to registration. * Age 18 to 75 years. * ECOG performance status 0, 1 or 2. * Life expectancy of ≥ 90 days (3 months). * Laboratory Requirements: (must be done within 7 days of registration) Hematology: * Granulocytes (AGC) ≥ 1.0 x 10\^9/L * Platelets ≥ 75 x 10\^9/L (≥ 50 if bone marrow involvement by lymphoma) Biochemistry: * AST and ALT ≤ 2.5x ULN (≤ 5x ULN if hepatic involvement of disease) * Serum total bilirubin ≤ 1.5x ULN (≤ 3x ULN if hepatic involvement of disease, or ≤5x ULN if Gilberts Disease) * Serum Potassium ≥ 3.8 mmol/L\* * Serum Magnesium ≥ 0.85 mmol/L\* \* NB: Patients with potassium and magnesium levels below these values are eligible if supplementation has corrected these deficits. This supplementation should continue throughout the course of the study. * Calculated creatinine clearance (Cockcroft-Gault formula) of ≥ 50 mL /min. * Women must be post-menopausal, surgically sterile or use reliable forms of contraception while on study and for 90 days after discontinuing therapy. Women of childbearing potential must have a pregnancy test taken and proven negative within 7 days prior to registration and must not be lactating. * Patient consent must be obtained according to local Institutional and/or University Human Experimentation Committee requirements. * Patients must be accessible for treatment and follow-up. Patients registered on this trial must be treated and followed at the participating centre. This implies there must be reasonable geographical limits (for example: 1 ½ hour's driving distance) placed on patients being considered for this trial. * In accordance with NCIC CTG policy, protocol treatment is to begin within 2 working days of patient registration. Exclusion Criteria: * Patients with a history of other malignancies, except: adequately treated non-melanoma skin cancer and superficial bladder cancer, curatively treated in-situ cancer of the cervix or breast or localized excised prostate cancer, or other solid tumours curatively treated with no evidence of disease for ≥ 3 years. * Central nervous system involvement, meningeal or parenchymal. Patients with CNS disease at initial presentation and who are in a CNS CR at the time of relapse are eligible. MRI scanning and / or lumbar puncture should be performed if there is clinical suspicion of active CNS disease. * HIV, active hepatitis B or current hepatitis C infection. (Hepatitis B core antibody positive, surface antigen negative patients allowed if concurrent anti-viral prophylaxis is administered. Patients with a past history of hepatitis C who have eradicated the virus are eligible.) * Any serious active disease or co-morbid medical condition, laboratory abnormality, or psychiatric illness that would prevent the patient from participating (according to investigator's decision). * Patients with serious cardiac illness or condition including, but not limited to: * history of documented congestive heart failure (CHF) * systolic dysfunction (LVEF \< 45% by MUGA or ECHO) * high risk uncontrolled arrhythmias (ventricular tachycardia, high-grade AV-block, supraventricular arrhythmias which are not adequately rate-controlled) * unstable angina pectoris requiring anti-anginal medication * clinically significant valvular heart disease * evidence of transmural infarction on ECG * New York Heart Association (NYHA) Class III or IV functional status * patients with congenital long QT syndrome, history of significant cardiovascular disease and/or taking drugs leading to significant QT prolongation * patients with QTc \> 480 msec are not eligible * Pregnant or lactating females or women of childbearing potential not willing to use an adequate method of birth control for the duration of the study. * Patients with active or uncontrolled infections, or with serious illnesses or medical conditions which would not permit the patient to be managed according to the protocol are not eligible. * Patients are not eligible if they have a known hypersensitivity to the study drugs or their components.