Rituximab, Romidepsin, and Lenalidomide in Treating Patients With Recurrent or Refractory B-cell Non-Hodgkin Lymphoma

Inclusion Criteria: * PHASE I: Histological confirmation of relapsed (recurrent after previous therapy\[ies\]) or refractory (no response to previous therapy\[ies\]) B-cell NHL; note: patients with small lymphocytic lymphoma (SLL) are eligible however patients with chronic lymphocytic leukemia (CLL) are not eligible * PHASE II: Histological confirmation of transformation of FL lymphoma to diffuse large B cell lymphoma or aggressive lymphoma * The biopsy confirming diagnosis can be up to 12 weeks prior to registration as long as there is no intervening therapy; note: if patient has had lymphoma treatment since previous biopsy, a biopsy should be repeated * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 * Measurable disease (at least 1 lesion of \>= 1.5 cm in diameter) as detected by computed tomography (CT) or the CT images of the positron emission tomography (PET)/CT * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelet count \>= 75,000/mm\^3 * Total bilirubin =\< 1.5 x upper limit of normal (ULN) or if total bilirubin is \> 1.5 x ULN, the direct bilirubin =\< ULN * Alkaline phosphatase =\< 3 x ULN unless due to direct lymphoma involvement, and then =\< 5 x ULN * Aspartate transaminase (AST) =\< 3 x ULN unless due to direct lymphoma involvement, and then =\< 5x ULN * Calculated creatinine clearance \>= 50 mL/min using the Cockcroft-Gault formula * Magnesium \>= 1.6 mg/dL * Potassium \>= 3.5 mg/dL * Females of reproductive potential must adhere to the scheduled pregnancy testing as required in the Revlimid Risk Evaluation and Mitigation Strategy (REMS)® program * Willing to be registered into the mandatory Revlimid REMS® program, and willing and able to comply with the requirements of the REMS® program * If currently not on anticoagulation medication, willing and able to take aspirin (325 mg) daily; note: if aspirin is contraindicated, the patient may be considered for the study after if on therapeutic dose warfarin or low molecular weight heparin; patients unable to take any prophylaxis are not eligible * Life expectancy \>= 3 months * Ability to complete medication diary by themselves or with assistance * Ability to provide informed written consent * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) * Note: during the active monitoring phase of a study (i.e., active treatment and observation), participants must be willing to return to the consenting institution for follow-up * Willing to provide tissue for central review and blood samples for correlative research purposes Exclusion Criteria: * Prior therapy with histone deacetylase (HDAC) inhibitors or immunomodulatory drugs (IMDs) (lenalidomide or thalidomide) * Any of the following: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * Active central nervous system (CNS) lymphoma or cerebrospinal fluid involvement with malignant lymphoma cells that requires therapy * Prolongation of corrected QT interval of \> 480 ms * Receiving any medications that prolong the corrected QT (QTc) and have a known risk for Torsades de pointes; note: providers should use caution with drugs with possible increased risk for Torsades de pointes; patient will be eligible if they can be taken off these medications prior to initiation of therapy and no less than 4 half-life of the medication * Receiving any medications or substances that are strong inhibitors of cytochrome P450, family 3, subfamily A, polypeptide 4/5 (CYP3A4/5) * Use of the following strong inhibitors are prohibited =\< 7 days prior to registration * Boceprevir (Victrelis™) * Clarithromycin (Biaxin®, Biaxin XL®) * Conivaptan (Vaprisol®) * Grapefruit juice * Indinavir (Crixivan®) * Itraconazole (Sporanox®) * Ketoconazole (Nizoral®) * Lopinavir/ritonavir (Kaletra®) * Mibefradil * Nefazodone (Serzone®) * Nelfinavir (Viracept®) * Posaconazole (Noxafil®) * Ritonavir (Norvir®) * Saquinavir (Invirase®) * Telaprevir (Incivek®) * Telithromycin (Ketek®) * Receiving any medications or substances that are inducers of CYP3A4 * Use of the following inducers are prohibited =\< 12 days prior to registration * Avasimibe * Bosentan (Tracleer®) * Carbamazepine (Carbatrol®, Epitol®, Equetro™, Tegretol®, Tegretol-XR®) * Efavirenz (Sustiva®) * Modafinil (Provigil®) * Phenobarbital (Luminal®) * Phenytoin (Dilantin®, Phenytek®) * Rifabutin (Mycobutin®) * Rifampin (Rifadin®) * St. John's wort * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Known positivity for human immunodeficiency virus (HIV); note: baseline testing for HIV is not required * 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; note: patients with hepatitis B and C are eligible at the discretion of the treating physician; appropriate counseling regarding the risks of rituximab should be provided * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * Other active malignancy requiring therapy; exceptions: non-melanotic skin cancer or any cancer that in the judgment of the investigator will not interfere with treatment plan and response assessment; patients with \>= 25% of the bone marrow radiated for other diseases are not eligible * History of myocardial infarction =\< 6 months prior to registration, unstable angina, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias * History of life threatening or recurrent thrombosis/embolism; patients may participate if they are on anticoagulation during the treatment * Receiving erythroid stimulating agents (erythropoietin \[EPO\]: Procrit, Aranesp) * History of allogeneic bone marrow or stem cell transplantation