Inclusion Criteria:

Patients must have histologically or cytologically confirmed indolent Non-Hodgkin's Lymphoma; included in this category are newly diagnosed or 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 vorinostat); Rituxan alone does not count as a regimen; however, Bexxar or Zevalin do; for treated patients, the most recent therapy must have failed to induce a complete response (i.e., there is persistent disease by CT or PET), 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 month post transplant; to be eligible after either type of transplant, patients 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 glutamic pyruvic transaminase [SGPT]) =< 2.5 x institutional upper limit of normal

Creatinine up to and including 2 mg/dl

Pre-menopausal women must have a negative serum pregnancy test prior to entry on this study; 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, 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 vorinostat; 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 vorinostat

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 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 mother is treated with vorinostat

Human immunodeficiency virus (HIV)-positive patients receiving combination antiretroviral therapy are ineligible; in addition, HIV patients not receiving combination antiretroviral therapy are also ineligible

Patients with other active malignancies are ineligible for this study

Patients with preexisting or previous coagulation issues are not excluded from study as long as 1) previous pulmonary embolism or deep vein thrombosis have been adequately treated or 2) if they are actively receiving Coumadin or lovenox for anticoagulation; patients who are already on coumadin or lovenox do not need to take additional 40 mg subcutaneous injections daily