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 childbea…