Bendamustine Hydrochloride, Rituximab, Etoposide, and Carboplatin in Treating Patients With Relapsed or Refractory Diffuse Large B-cell Lymphoma or Hodgkin Lymphoma

Inclusion Criteria: * Patients must have relapsed or primary refractory lymphomas: diffuse large B cell lymphoma (DLBCL) or Hodgkin's lymphoma (HL); patients with other lymphoid malignancies such as T- cell, or lymphomas that are not curable with anthracycline based therapy (e.g. mantle cell lymphoma \[MCL\], follicular lymphoma \[FL\], marginal zone lymphoma \[MZL\], lymphoplasmacytic lymphoma \[LPL\]) are eligible with protocol Chair review and approval; Note: as of 11/1/12 only patients with typical DLBCL and HL are eligible for enrollment; unusual pathology for DLBCL and HL will require Study Chair approval; the goal is to have 20 patients with DLBCL and 20 patients with HL enrolled * 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; Note: CT scans remain the standard for evaluation of nodal disease * Patients must have a CT of chest, abdomen, and pelvis within 28 days of enrollment; patients with evidence of lymphadenopathy in the neck must have a CT of neck * Patients should not have evidence of active central nervous system lymphoma * Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 (without transfusion or growth factor support); exception: patients with cytopenias due to disease, that do not meet these criteria, will be considered eligible with review and approval by the principal investigator (PI) or Co-PI prior to study entry * Platelets \>= 100,000/mm\^3 (without transfusion or growth factor support); exception: patients with cytopenias due to disease, that do not meet these criteria, will be considered eligible with review and approval by the PI or Co-PI prior to study entry * Serum creatinine \< 1.5 mg/dl or creatinine clearance greater than 50/ml per minute * Total bilirubin \< 1.5 times upper limit of normal * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 2.5 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 Exclusion Criteria: * Patients known positive for human immunodeficiency virus (HIV), or infectious hepatitis type B or C * 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, breast or 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 * Patients who are refractory (i.e. not responded or progressed within 6 months) to a carboplatin, cisplatin, bendamustine, or etoposide-based regimen * Patients who 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, uncontrolled arrhythmia); if the patient's cardiac 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; prior failed (\< 5 x 10\^6 CD34/kg) peripheral blood stem cell (PBSC) collection * Patients who had pelvic radiation within 12 months or received more than 2 prior therapies with myelotoxic regimens; single agent monoclonal antibody treatment is not considered as one therapy; radiation treatment following chemotherapy is not considered as one separated therapy; consolidative therapy will be considered one regimen e.g. salvage therapy followed by conditioning regimen and transplant * Previous chemotherapy/immunotherapy within 3 weeks before study entry * Concurrent use of other anti-cancer agents or experimental treatments * Known hypersensitivity to bendamustine, mannitol, etoposide, carboplatin, or rituximab