Vorinostat, Rituximab, Ifosfamide, Carboplatin, and Etoposide in Treating Patients With Relapsed or Refractory Lymphoma or Previously Untreated T-Cell Non-Hodgkin Lymphoma or Mantle Cell Lymphoma

Inclusion Criteria: * Patients must have relapsed or primary refractory lymphoid malignancy (including B-cell, T-cell, or Hodgkins disease), or untreated T-NHL or MCL * Patients with other lymphomas that have not received any prior therapy and are not candidates for anthracycline-based therapies, are eligible with PI review and approval * Revised European American classification (REAL), or World Health Organization (WHO) classification of patient's malignancies must be provided * Patients must have measurable disease defined as lesions that can be accurately measured in two dimensions by computed tomography (CT), magnetic resonance imaging (MRI), medical photograph (skin or oral lesion), plain x-ray, or other conventional technique and a greatest transverse diameter of 1 cm or greater; or palpable lesions with both diameters \>= 2 cm * Patients must have a bone marrow aspirate and biopsy within 28 days of enrollment and no intervening anticancer therapy * Patients must have a CT of chest, abdomen, and pelvis within 28 days of enrollment; patients with evidence of adenopathy in the neck must have a CT of neck * Patients should not have evidence of active central nervous system lymphoma * Electrocardiogram (EKG) must be free of any arrhythmias (excluding sinus arrhythmia or infrequent premature ventricular contractions) * Patients must have a Southwest Oncology Group (SWOG) performance status of 0, 1, or 2 * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 * Serum creatinine \<…