Bortezomib and Vorinostat in Treating Patients With Recurrent Mantle Cell Lymphoma or Recurrent and/or Refractory Diffuse Large B-Cell Lymphoma

Inclusion Criteria: * Histologically confirmed mantle cell or diffuse large B-cell lymphoma; histological material must be available for central pathological review; unstained histological material -- slides or blocks -- must be available for correlative studies; archived material from previous biopsies is acceptable, unless a patient's lymphoma has been known to undergo histological transformation in the past, in which case a repeat biopsy to confirm histology prior to enrollment is required; availability of material must be confirmed at the time of registration, but material may be submitted subsequent to registration and initiation of study treatment * Measurable disease according to the Revised Response Criteria for Malignant Lymphoma; this requires at least one lesion greater than 1.0 cm in diameter in both the long and short axis as measured by spiral computed tomography (CT) scan or physical exam * Prior allogeneic stem cell transplant is allowed provided that all of the following conditions are met: * \>= 6 months have elapsed since allogeneic transplant * No graft vs. host disease (GVHD) is present * Not currently on immunosuppressive therapy * Prior therapy: * Mantle cell lymphoma: * Previously treated or untreated * No prior bortezomib * Diffuse large B-cell lymphoma: * At least one prior systemic therapy * No prior bortezomib * Note: Not intended for patients in first relapse who are candidates for high dose therapy with stem cell support * Life expectancy of greater than 3 months * Eastern Cooperative Oncology Group (ECOG) performance status 0, 1, or 2 * Able to tolerate loperamide or other anti-diarrheal medications * Absolute neutrophil count \>= 1.5 x 10\^9/L * Platelets \>= 75 x 10\^9/L * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transferase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal * Creatinine within normal institutional limits or calculated creatinine clearance \>= 60 mL/min according to the Cockcroft-Gault formula * For patients with known human immunodeficiency virus (HIV) infection, a cluster of differentiation (CD)4 count \>= 0.5 x 10\^9/L * For patients whose last treatment included bendamustine or fludarabine, a CD4 count \>= 0.4 x 10\^9/L * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation and to report pregnancy or suspected pregnancy while participating in the study * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Chemotherapy or large field radiotherapy within 3 weeks prior to entering the study * Prior histone deacetylase inhibitor as cancer treatment * Concurrent treatment with other investigational agents * Plans for other concurrent cancer treatment; if steroids for cancer control have been used, patients must be off these agents for \>= 1 week before starting treatment; exception: maintenance therapy for non-malignant disease with prednisone or steroid equivalent dose \< 10 mg/day is permitted * History of brain metastasis including leptomeningeal metastasis * Grade \>= 2 neuropathy, regardless of cause * Unable to take oral medications * History of allergic reactions attributed to compounds of similar chemical or biologic composition to bortezomib or vorinostat * Not sufficiently recovered from previous treatment * Medical or other condition (for example: uncontrolled infection; potentially life threatening changes on electrocardiogram \[EKG\]) or concurrent treatment (for example, marrow suppressive agents such as zidovudine) that represents an inappropriate risk to the patient or likely would compromise achievement of the primary study objective; patients should be closely monitored when given bortezomib in combination with the cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) inhibitors and inducers * Pregnant women are excluded from this study; breastfeeding should be discontinued * Active concurrent malignancy, except adequately treated non-melanoma skin cancer