Lenalidomide, Ixazomib, and Rituximab as Front-Line Therapy for High Risk Indolent B-Cell Lymphoma

Inclusion Criteria: * Patients must have histologically confirmed, low-grade B-lymphocyte Non-Hodgkin's Lymphoma (NHL) by the World Health Organization Classification: * Follicular lymphoma grades 1, 2, and 3a * Marginal zone B-cell lymphoma, including extranodal (MALT), nodal and splenic. Excluding: Small lymphocytic lymphoma Lymphoplasmacytic lymphoma/Waldenström's macroglobulinemia (WM) * Lymphoplasmacytic lymphoma (including Waldenström's macroglobulinemia (WM)) * Must have stage 2, 3 or 4 disease, with either high tumor burden by Groupe d'Etude des Lymphomes Folliculaires (GELF) criteria and/or Follicular Lymphoma International Prognostic Index (FLIPI) 3-5 * To meet GELF criteria, patient must have at least one criterion: * Nodal or extranodal mass \> 7 cm * At least 3 nodal masses: each \> 3.0 cm in longest dimension * Systemic symptoms due to lymphoma or B symptoms * Splenomegaly with spleen \> 16 cm by Computed Tomography (CT) scan * Evidence of compression syndrome (e.g., ureteral, orbital, gastrointestinal) or pleural or peritoneal serous effusion due to lymphoma (irrespective of cell content) * Leukemic presentation (\> 5.0 x 10\^9/L malignant circulating follicular or lymphoma cells) * Cytopenias (absolute neutrophil count \< 1.0 X 10\^9/L, hemoglobin \< 10 gm/dL, and/or platelets \<100 x 10\^9/L). * AND/OR To meet FLIPI criteria, patient must have at least 3 out of the following 5 criteria: * Age \> 60 years * Ann Arbor stage III-IV * Hemoglobin level \< 12 mg/dL * ≥ 5 nodal areas * Serum Lactate Dehydrogenase (LDH) level above normal * Must have previously untreated lymphoma. A short (\< 2 week) course of steroids for symptom palliation is permitted. Prior involved field radiotherapy for symptom palliation is permitted as long as there is measurable disease outside the radiation port. If radiotherapy has been given, there should be at least 7 days between last treatment and beginning of protocol therapy. * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension * Eastern Cooperative Oncology Group (ECOG) performance status 0, 1, or 2. * Patients must have adequate hematologic, hepatic, and renal function as defined below: * Absolute neutrophil count (ANC) ≥ 1,000/mcL * Platelet count ≥ 75,000/mcL * Total bilirubin ≤ 1.5 x the upper limit of the normal range (ULN) * Aspartate Aminotransferase (AST) (SGOT) ≤ 3 x institutional upper limit of normal * Alanine Aminotransferase (ALT) (SGPT) ≤ 3 x institutional upper limit of normal * Calculated creatinine clearance ≥ 30 mL/min/1.73 m\^2 * Participants must agree to ongoing anticoagulation as prophylaxis against deep vein thrombosis (DVT) using aspirin (81 or 325 mg) daily, warfarin or low molecular weight heparin, or a patient already taking another oral anticoagulant (e.g. direct thrombin inhibitors for atrial fibrillation) may continue that agent. * All study participants must be willing to register with the mandatory RevAssist program and be willing to comply with its requirements. * 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. * A woman of childbearing potential must agree to practice: * 2 effective methods of contraception, at the same time, from the time of signing the informed consent form through 90 days after the last dose of study drug, OR * True abstinence when this is in line with the preferred and usual lifestyle of the subject. * A woman of childbearing potential must have a negative serum or urine pregnancy test with a sensitivity of at least 50 mIU/mL within 10-14 days prior to and again within 24 hours of starting therapy with Revlimid®. Females of reproductive potential must adhere to the scheduled pregnancy testing as required in the Revlimid REMS® program. * Male patients, even if surgically sterilized (i.e., status post-vasectomy), must agree to one of the following: * Agree to practice effective barrier contraception during the entire study treatment period and through 90 days after the last dose of study drug, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. * Subjects must have the ability to understand and the willingness to sign a written informed consent document and HIPAA consent document. Voluntary written consent must be given before performance of any study related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care. Exclusion Criteria: * Patients who are receiving any other investigational agents. * Female patients who are lactating or have a positive serum pregnancy test during the screening period. * Major surgery within 14 days before enrollment. * Radiotherapy within 14 days before enrollment. If the involved field is small (single nodal area), 7 days will be considered a sufficient interval between treatment and beginning of protocol therapy. * Known central nervous system involvement. * Infection requiring systemic antibiotic therapy or other serious infection within 14 days before study enrollment. * Evidence of current uncontrolled cardiovascular conditions, including uncontrolled cardiac arrhythmias, symptomatic congestive heart failure, unstable angina, or myocardial infarction within the past 6 months. * Systemic treatment, within 14 days before the beginning of protocol therapy, with CYP3A inducers (rifampin, rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital), or use of St. John's wort. * Known allergy to any of the study medications, their analogues, or excipients in the various formulations of any agent. Specifically, prior desquamating rash or erythema nodosum during prior thalidomide or other similar agents. * Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral absorption or tolerance of ixazomib or lenalidomide including difficulty swallowing. * Diagnosed or treated for another malignancy within 2 years before study enrollment or previously diagnosed with another malignancy and have any evidence of residual disease. Patients with non-melanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone complete resection. * Patient has ≥ Grade 2 peripheral neuropathy on clinical examination during the screening period. * Participation in other clinical trials, including those with other investigational agents not included in this trial, within 30 days of the start of this trial and throughout the duration of this trial. * Any prior use of Revlimid® or Velcade®. * Known seropositivity for, or active viral infection with, Human Immunodeficiency Virus (HIV), Hepatitis B Virus (HBV) (unless due to vaccination), or Hepatitis C Virus (HCV). HIV-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with lenalidomide and ixazomib. In addition, these patients are at increased risk of lethal infections when treated with marrow suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated. * Pregnant or breastfeeding women are excluded from this study because lenalidomide has known teratogenic effects. Because there is an unknown, but potential risk for adverse events in nursing infants secondary to treatment of the mother with lenalidomide, breastfeeding should be discontinued if the mother is treated with lenalidomide. These potential risks may also apply to other agents used in this study.