Brief Summary: 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.

Detailed Description: 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.