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 \< 1.5 mg/dl or creatinine clearance greater than 60/ ml per minute by the following formula (all tests must be performed within 28 days prior to registration) * Total bilirubin \< 1.5 times upper limit of normal, aspartate aminotransferase (AST) \< 5 times upper limit of normal * Patients must have a serum lactate dehydrogenase (LDH) performed within 14 days prior to registration * All patients must be informed of the investigational nature of this study and have given written consent in accordance with institutional and federal guidelines * Patients must be anticipated to complete at least 2 cycles of chemotherapy * Platelets \>= 100,000/mm\^3 (without transfusion) Exclusion Criteria: * Patients known to be human immunodeficiency virus (HIV) positive * Pregnant or nursing women; men or women of reproductive potential may not participate unless they have agreed to use an effective contraceptive method * Patients with other prior malignancies except for adequately treated basal cell carcinoma, squamous cell carcinoma of the skin, cervical cancer in situ, or other cancer from which the patient has been disease free for 5 years or greater, unless approved by the protocol Chair or Co-Chair * Patients that are refractory (i.e. not responded or progressed within 6 months) to a carboplatin, cisplatin, ifosfamide, or etoposide-based regimen-based regimen * Patients that have other medical conditions that would contraindicate treatment with aggressive chemotherapy (including active infection, uncontrolled hypertension, congestive heart failure, unstable angina pectoris, or myocardial infarction within the past 6 months, or uncontrolled arrhythmia) * Patients with a history of impaired cardiac status (including history of severe coronary artery disease, cardiomyopathy, congestive heart failure or arrhythmia); if the patient's history is questionable, a measurement of left ventricular ejection fraction should be obtained within 42 days prior to registration; patients with left ventricular ejection fraction \< 50% are not eligible * Autologous or allogeneic transplantation within 12 months or radioimmunotherapy within 6 months of registration * No concurrent treatment with valproic acid or on valproic acid within 2 weeks of study enrollment * No prior treatment with histone deacetylase inhibitors * No concurrent therapy for this malignancy