This phase I trial studies the best dose and side effects of romidepsin when given in combination with ifosfamide, carboplatin, and etoposide in treating participants with peripheral T-cell lymphoma that has come back or does not respond to treatment. Romidepsin may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as ifosfamide, carboplatin, and etoposide, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving romidepsin, ifosfamide, carboplatin, and etoposide may work better in treating participants with peripheral T-cell lymphoma.

PRIMARY OBJECTIVES:

I. To assess the safety profile of romidepsin given before and after ifosfamide, carboplatin, etoposide (ICE) chemotherapy for patients with relapsed or refractory peripheral T-cell lymphoma (PTCL).

II. To determine the maximum tolerated dose (MTD), if reached, of romidepsin administered in combination with ICE chemotherapy in patients with relapsed or refractory PTCL.

SECONDARY OBJECTIVES:

I. To determine the overall response rate (ORR) and complete response (CR) rate in patients with relapsed or refractory PTCL.

OUTLINE: This is a dose-escalation study of romidepsin.

Participants receive romidepsin intravenously (IV) over 4 hours on days 1 and 4, ifosfamide IV over 24 hours on day 1, carboplatin IV over 1 hour on day 1, and etoposide IV over 2 hours on day 1-3. Treatment repeats every 14 days for up to 6 courses in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, participants are followed up within 2-4 weeks.

Inclusion Criteria:

• Relapsed or refractory T cell lymphoma (TCL) status including diagnoses of peripheral TCL-not otherwise specified (NOS), angioimmunoblastic TCL, anaplastic large cell lymphoma, hepatosplenic TCL, enteropathy-associated TCL, or mycosis fungoides(MF)/cutaneous TCL with transformation to systemic TCL
• Patients must have received at least one chemotherapy regimen which contained doxorubicin
• At least one 1.5 cm bidimensional measurable lesion or bone marrow positivity of TCL
• Eastern Cooperative Oncology Group (ECOG) performance status =< 2
• Absolute neutrophil count (ANC) >= 1000 cells/mm3
• Platelets >= 80,000 cells/mm3 if baseline bone marrow negative for TCL involvement and platelets >= 20,000 cells/mm3 if baseline bone marrow positive for TCL involvement
• Bilirubin =< 2 x upper limits of normal (ULN) (Gilbert's =< 3 x upper limit of normal [ULN])
• Creatinine =< 1.5 x ULN
• Alanine aminotransferase (ALT) and aminotransferase (AST) =< 3 x ULN
• Negative pregnancy test for females of childbearing potential within 7 days prior to start of treatment. Patients of reproductive potential must follow accepted birth control methods which include hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence during treatment and for 3 months after completion of treatment
• Voluntarily signed Institutional Review Board (IRB) approved informed consent document (ICD) before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care

Exclusion Criteria:

• History of another malignancy not in remission for at least 2 years (yrs) (except non-melanoma skin cancer, stage 0 melanoma, localized prostate cancer, cervical cancer in situ)
• Known active Central Nervous System (CNS) lymphoma
• Ejection fraction (EF) of < 40%, myocardial infarction (MI) within past 3 months, uncontrolled angina, severe uncontrolled ventricular arrthymias, or electrocardiogram (ECG) evidence of acute ischemia
• Grade 3 infection within 2 weeks of first dose romidepsin plus ICE
• Pregnant or lactating
• Receipt of another investigational drug within 14 days of enrollment
• Patients with previous hypersensitivity reactions to the study drugs and components (ex: podophyllum and povidone)