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