Obatoclax and Bortezomib in Treating Patients With Aggressive Relapsed or Recurrent Non-Hodgkin Lymphoma

Inclusion Criteria: * Histologically or cytologically confirmed relapsed or refractory non-Hodgkin lymphoma for which standard curative or palliative measures do not exist or are no longer effective, including any of the following subtypes: * Follicular grade I, II, or III lymphoma * Marginal zone lymphoma * Mantle cell lymphoma * Diffuse large B cell lymphoma * Small lymphocytic lymphoma * Must have had at least one prior chemotherapeutic regimen: * Steroids or rituximab alone or local radiotherapy do not count as regimens * Tositumomab or ibritumomab tiuxetan allowed as regimens * Clear evidence of disease progression or lack of response after the most recent therapy, including rituximab or local radiotherapy, is required * At least 3 months since prior autologous stem cell transplantation and relapsed (\>= 1 year since prior allogeneic transplantation and relapsed) and no active related infections (i.e., fungal or viral) * In the case of allogeneic transplantation relapse, there should be no active acute graft-versus-host disease (GVHD) of any grade and no chronic GVHD other than mild skin, oral, or ocular GVHD not requiring systemic immunosuppression * No known active brain metastases, other neurological disorders/dysfunction or history of seizure disorder, or other neurological dysfunction * Karnofsky performance status 60-100% * Life expectancy \> 3 months * Total bilirubin normal * AST and ALT =\< 2.5 times upper limit of normal * Creatinine normal or creatinine clearance \>= 60 mL/min * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective double-barrier contraception during and for 3 months after the last dose of obatoclax mesylate * At least 4 weeks since prior radiotherapy * More than 2 days since prior steroids * More than 2 weeks since prior low-dose chlorambucil * WBC \>= 3,000/mm\^3 * ANC \>= 1,500/mm\^3 * Platelet count \>= 100,000/mm\^3 * At least 2 weeks since prior valproic acid Exclusion Criteria: * Uncontrolled concurrent medical condition or illness including, but not limited to, any of the following: * Ongoing or active infection * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia including QTc \> 450 msec * Patients who are intolerant or refractory to prior treatment with bortezomib (refractory is defined as no response to prior treatment with bortezomib) * Chemotherapy within the past 4 weeks (6 weeks for nitrosoureas or mitomycin C) * Rituximab within the past 3 months (unless there is evidence of progression) * Patients who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Other concurrent investigational agents * Combination antiretroviral therapy for HIV-positive patients * No history of allergic reactions attributed to bortezomib, polyethylene glycol (PEG 300), or polysorbate 20 * No psychiatric illness or social situation that would limit compliance with study requirements