Lenalidomide and Obinutuzumab in Treating Patients With Relapsed Indolent Non-Hodgkin Lymphoma

Inclusion Criteria: * A diagnosis of small lymphocytic lymphoma, follicular lymphoma (grades 1-3a), or marginal zone lymphoma * Evidence of progression or lack of response following at least 1 prior treatment for indolent lymphoma * Able and willing to provide written informed consent and to comply with the study protocol * Must have at least 1 node greater than 1.5 cm in short axis diameter * Adequate hematologic function (unless abnormalities are related to NHL), defined as follows: * Hemoglobin \>= 9.0 g/dL * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L; ANC \< 1.5 x 10\^9/L if cytopenia is due to extensive bone marrow involvement of disease as determined by the treating physician * Platelet count (PLT) \>= 75 x 10\^9/L; PLT count less than 100 x 10\^9/L if cytopenia is due to extensive bone marrow involvement of disease as determined by the treating physician * For men who are not surgically sterile, agreement to use a barrier method of contraception for \>= 3 months after the last obinutuzumab dose; in addition, male patients must agree to request that their partners use an additional method of contraception, such as oral contraceptives, intrauterine device, barrier method of contraception, or spermicidal jelly * For women of reproductive potential who are not surgically sterile, agreement to use two adequate methods of contraception, such as oral contraceptives, intrauterine device, or barrier method of contraception in conjunction with spermicidal jelly for \>= 12 months after the last obinutuzumab dose * Females of childbearing potential (FCBP) must have a negative serum pregnancy test with a sensitivity of at least 50 mIU/mL within 10-14 days prior to and again within 24 hours of prescribing lenalidomide and must either commit to continued abstinence from heterosexual intercourse or begin TWO acceptable methods of birth control, one highly effective method and one additional effective method AT THE SAME TIME, at least 4 weeks before she starts taking lenalidomide; FCBP must also agree to ongoing pregnancy testing; men must agree to use a latex condom during sexual contact with a female of child bearing potential even if they have had a successful vasectomy * A female of childbearing potential is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) * All study participants must be registered into the mandatory Revlimid Risk Evaluation and Mitigation Strategy (REMS) program, and be willing and able to comply with the requirements of Revlimid REMS program * For patients with bulky disease (tumors \> 5 cm); must be able to take aspirin (81 mg or 325 mg) daily as prophylactic anticoagulation (patients intolerant to acetylsalicylic acid \[ASA\] may use warfarin or low molecular weight heparin) * Females of reproductive potential must adhere to the scheduled pregnancy testing as required in the Revlimid REMS program; able to take aspirin (81 or 325 mg) daily as prophylactic anticoagulation (patients intolerant to ASA may use warfarin or low molecular weight heparin) Exclusion Criteria: * Evidence ongoing transformation into aggressive NHL * History of severe allergic or anaphylactic reactions to monoclonal antibody therapy * Known hypersensitivity to thalidomide or lenalidomide * Regular treatment with corticosteroids during the 4 weeks prior to the start of cycle 1, unless administered for indications other than NHL at a dose equivalent to =\< 30 mg/day prednisone * History of prior malignancy within the last 5 years, with the exception of curatively treated basal or squamous cell carcinoma of the skin and low-grade in situ carcinoma of the cervix * Evidence or history of significant, uncontrolled concomitant diseases that could affect compliance with the protocol or interpretation of results, including significant cardiovascular disease (such as New York Heart Association class III or IV cardiac disease, severe arrhythmia, myocardial infarction within the previous 6 months, unstable arrhythmias, or unstable angina) or pulmonary disease (including obstructive pulmonary disease and history of bronchospasm) * Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection (excluding fungal infections of nail beds) or any major episode of infection requiring treatment with IV antibiotics or hospitalization (relating to the completion of the course of antibiotics, except if for tumor fever) within 4 weeks prior to the start of cycle 1; patients with suspected active or latent tuberculosis (latent tuberculosis needs to be confirmed by positive interferon-gamma release assay) * Vaccination with live vaccines within 28 days prior to start of treatment * Any of the following abnormal laboratory values (unless any of these abnormalities are due to underlying lymphoma) * Creatinine \> 1.5 times the upper limit of normal (ULN) (unless creatinine clearance normal), or calculated creatinine clearance \< 40 mL/min (using Cockcroft-Gault formula) * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \> 2.5 x ULN * Total bilirubin \> 1.5 x ULN (or \> 3 x ULN for patients with documented Gilbert syndrome) * Any history of hepatitis B infection * Positive test results for hepatitis C (hepatitis C virus \[HCV\] antibody serology testing); patients positive for HCV antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA) * Known history of human immunodeficiency virus (HIV) seropositive status * Positive test results for human T-lymphotropic 1 (HTLV 1) virus; HTLV testing is required in patients from endemic countries (Japan, countries in the Caribbean basin, South America, Central America, Sub Saharan Africa, and Melanesia) * Pregnant or lactating * Eastern Cooperative Oncology Group (ECOG) performance status greater than 2 * Participation in another clinical trial with drug intervention within 21 days prior to start of cycle 1 and during the study * Patients with small lymphocytic lymphoma (SLL)/chronic lymphocytic leukemia (CLL) are excluded during the phase I portion of the study