Ibrutinib in Combination With Rituximab and Lenalidomide in Treating Patients With Previously Untreated, Stage II-IV Follicular Lymphoma or Marginal Zone Lymphoma

Inclusion Criteria: * Histologically confirmed CD20+ follicular lymphoma, grade 1, 2, or 3a or marginal zone lymphoma * Have had no prior systemic treatment for lymphoma * Bi-dimensionally measurable disease, with at least one mass lesion \>= 2 cm in longest diameter by computed tomography (CT), positron emission tomography (PET)/CT, and/or magnetic resonance imaging (MRI) * In the opinion of the investigator would benefit from systemic therapy * Stage II, III, or IV disease * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Absolute neutrophil count (ANC) \>= 1,000/mm\^3, independent of growth factor support (within 28 days prior to signing informed consent). * Platelet counts \>= 100,000/mm\^3 or \>= 50,000/mm\^3 if bone marrow involvement with lymphoma, independent of transfusion support in either situation (within 28 days prior to signing informed consent). * Serum aspartate transaminase (AST) or alanine transaminase (ALT) \< 3 x upper limit of normal (ULN) * Creatinine clearance \> 30 ml/min calculated by modified Cockcroft-Gault formula * Bilirubin \< 1.5 x ULN unless bilirubin is due to Gilbert's syndrome, documented liver involvement with lymphoma, or of non-hepatic origin, in which case bilirubin should not exceed 3 g/dL * Prothrombin time (PT)/international normalized ratio (INR) \< 1.5 x ULN and partial thromboplastin time (PTT) \< 1.5 x ULN * Must be able to adhere to the study visit schedule and other protocol requirements * Women of childbearing potential and men who are sexually active must be practicing a highly effective method of birth control during and after the study; females of childbearing potential: must either completely abstain from heterosexual sexual conduct or must use 2 methods of reliable contraception, 1 highly effective (intrauterine device, birth control pills, hormonal patches, injections, vaginal rings, or implants) and at least 1 additional method (condom, diaphragm, cervical cap) of birth control; reliable contraceptive methods must be started at least 4 weeks before lenalidomide; males who are sexually active must be practicing complete abstinence or agree to a condom during sexual contact with a pregnant female or female of child bearing potential; men must agree to not donate sperm during and after the study; for females, these restrictions apply at least 4 weeks before study treatment, during the period of therapy and for 1 month after the last dose of study drug; for males, these restrictions apply during the period of therapy and for 3 months after the last dose of study drug * Women of childbearing potential must have a negative serum (beta-human chorionic gonadotropin \[Beta-hCG\]) pregnancy test at screening; women who are pregnant or breastfeeding are ineligible for this study; females of reproductive potential must adhere to the scheduled pregnancy testing as required in the Revlimid Risk Evaluation and Mitigation Strategy (REMS) program * Sign (or their legally-acceptable representatives must sign) an informed consent document indicating that they understand the purpose of and procedures required for the study, including biomarkers, and are willing to participate in the study * All study participants must be registered into the mandatory Revlimid REMS program, and be willing and able to comply with the requirements of the REMS program Exclusion Criteria: * Known central nervous system lymphoma or leptomeningeal disease, except subjects with a history of central nervous system lymphoma treated and in remission \> 6 months * Evidence of diffuse large B-cell transformation * Grade 3b FL * Any prior history of other malignancy besides FL or marginal zone lymphoma, unless the patient has been free of disease for \>= 5 years and felt to be at low risk for recurrence by the treating physician, except: * Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease * Adequately treated cervical carcinoma in situ without evidence of disease * Any life-threatening illness, medical condition, or organ system dysfunction which, in the investigator's opinion, could compromise the subject's safety, interfere with the absorption or metabolism of ibrutinib capsules, or put the study outcomes at undue risk, including but not limited to: * Moderate to severe hepatic impairment (Child-Pugh classes B and C) * Known history of human immunodeficiency virus (HIV) or active hepatitis C virus or active hepatitis B virus infection, or any uncontrolled active systemic infection * Patients with inactive hepatitis B infection must adhere to hepatitis B reactivation prophylaxis unless contraindicated * Prior use of ibrutinib or other BTK inhibitors, rituximab or lenalidomide * Concurrent systemic immunosuppressant therapy (e.g., cyclosporine, tacrolimus, etc., or chronic administration glucocorticoid equivalent of \> 10 mg/day of prednisone) within 28 days of the first dose of study drug * Known anaphylaxis or immunoglobulin E (IgE)-mediated hypersensitivity to murine proteins or to any component of rituximab * Requires anticoagulation with warfarin or equivalent vitamin K antagonists (e.g., phenprocoumon); if patients have been on warfarin or equivalent vitamin K antagonists in the past, they will not be eligible if administered within 30 days of the first dose of study drug * Requires chronic treatment with strong CYP3A inhibitors; if patients have been on a strong CYP3A inhibitor in the past, they will not be eligible if the CYP3A inhibitor was administered within 7 days of the first dose of study drug * Requires chronic treatment with strong CYP3A inducers, for a list of strong CYP3A inducers, see the protocol. If patients have been on a strong CYP3A inducer in the past, they will not be eligible if the CYP3A inducer was administered within 7 days of the first dose of study drug * Clinically significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of screening, or any class 3 (moderate) or class 4 (severe) cardiac disease as defined by the New York Heart Association Functional classification * Significant screening electrocardiogram (ECG) abnormalities including left bundle branch block, 2nd degree atrioventricular (AV) block, type II AV block, or 3rd degree block * Known bleeding diathesis (e.g., von Willebrand's disease) or hemophilia * History of stroke or intracranial hemorrhage within 6 months prior to study entry * Vaccinated with live, attenuated vaccines within 4 weeks of study entry * Lactating or pregnant subjects * Administration of any investigational agent within 28 days of first dose of study drug * Patients who have undergone major surgery within 7 days or minor surgery within 3 days of first dose of study drug