Vorinostat in Treating Patients With Low-Grade Non-Hodgkin's Lymphoma

Inclusion Criteria:

* Patients must have histologically or cytologically confirmed relapsed/refractory indolent Non-Hodgkin's lymphoma (Included in this category are relapsed/refractory follicular center lymphomas grade I, II, III, relapsed /refractory marginal zone B-cell lymphoma (nodal and extranodal), relapsed/refractory mantle cell lymphoma)
* Patients must have measurable disease by computed tomography (CT) scan. positron emission tomography (PET) scan evaluations are desirable but not mandatory, so that patients with negative PET scans but measurable disease by CT are eligible
* Patients may have had up to four prior chemotherapeutic regimens; steroids alone and local radiation do not count as regimens (radiotherapy must have been completed at least 14 days prior to starting SAHA); rituxan alone does not count as a regimen, however, Bexxar or Zevalin do; the most recent therapy must have failed to induce a complete response, or there must be disease progression or recurrence after the most recent therapy
* Patients may be enrolled who relapse after autologous stem cell transplant if they are at least three months after transplant, and after allogeneic transplant if they are at least six months post transplant; to be eligible after either type of transplant, patients must have achieved platelet counts greater than 100,000/mcL, and white blood cell (WBC) greater than 1,000/mcL at some point after their transplant, and should have no active related infections (i.e. fungal or viral); in the case of allogeneic transplant relapse, there should be no active acute graft versus host disease (GvHD) of any grade, and no chronic graft versus host disease other than mild skin, oral, or ocular GvHD not requiring systemic immunosuppression
* Life expectancy of greater than 3 months
* Eastern Cooperative Oncology Group (ECOG) performance status #2 (Karnofsky \>= 60%)
* Absolute neutrophil count \>= 1,000/mcL
* Platelets \>= 100,000/mcL
* Total bilirubin within normal institutional limits; patients with elevation of unconjugated bilirubin alone, as in Gilbert's Disease, are eligible
* Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT)(serum glutamate pyruvate \[SGPT\]) =\< 2.5 x institutional upper limit of normal
* Creatinine up to and including 2 mg/dl
* Premenopausal women must have a negative serum pregnancy test prior to entry on this study; the effects of SAHA on the developing human fetus at the recommended therapeutic dose are unknown; 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; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately
* Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

* Patients who have had chemotherapy within 4 weeks, rituximab within three months (unless there is evidence of progression) or radiotherapy within 2 weeks or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier are excluded; this does not include use of steroids, which may continue until two days prior to enrollment; low dose chlorambucil should be stopped two weeks prior to beginning SAHA; valproic acid should be stopped at least two weeks prior to enrollment; nitrosoureas and mitomycin should be stopped 6 weeks prior to enrollment
* Patients may not be receiving any other investigational agents
* Patients with known brain metastases are excluded from this clinical trial unless the metastases are controlled after therapy and have not been treated with steroids within the past two months
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to SAHA
* There must be no plans for the patient to receive concurrent hormonal, biological or radiation therapy
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with SAHA
* Human immunodeficiency virus (HIV)-positive patients receiving combination antiretroviral therapy are ineligible
* Patients with other active malignancies are ineligible for this study