Romidepsin, Ifosfamide, Carboplatin, and Etoposide in Treating Participants With Relapsed or Refractory Peripheral T-Cell Lymphoma

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performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care Exclusion Criteria: * History of another malignancy not in remission for at least 2 years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)