Rituximab, Bendamustine Hydrochloride, and Bortezomib Followed by Rituximab and Lenalidomide in Treating Older Patients With Previously Untreated Mantle Cell Lymphoma

Step 1 (Induction) Inclusion Criteria: * Mantle Cell Lymphoma International Prognostic Index (MIPI) score must be calculated and entered in OPEN * Histologically confirmed untreated mantle cell lymphoma (MCL), with documented cyclin D1 by immunohistochemical stains and/or t(11;14) by cytogenetics or fluorescence in situ hybridization (FISH) * Patients must have at least one objective measurable disease parameter * Negative pregnancy test * Women of childbearing potential and sexually active males use an accepted and effective method of contraception * ECOG performance status 0-2 * Absolute neutrophil count (ANC) ≥ 1,500/mcL (1.5 x 10\^9/L) * Platelets ≥ 100,000/mcL (100 x 10\^9/L) * Aspartate transaminase (AST)/alanine transaminase (ALT) ≤ 2 times upper limit of normal (ULN) * Bilirubin ≤ 2 times ULN * Calculated creatinine clearance by Cockroft-Gault formula ≥ 30 mL/min * Patient agrees that if randomized to Arms C or D, and proceeding onto Arms G or H, they must register into the mandatory RevAssist program, and be willing and able to comply with the requirements of RevAssist. Patients must have no medical contra-indications to, and be willing to take, DVT prophylaxis as all patients registering to the lenalidomide/rituximab Arms G and H will be required to have deep vein thrombosis (DVT) prophylaxis. Patients randomized to Arms G or H who have a history of a thrombotic vascular event will be required to have full anticoagulation, therapeutic doses of low molecular weight heparin or warfarin to maintain an INR between 2.0 - 3.0, or any other accepted full anticoagulation regimen (e.g. direct thrombin inhibitors or Factor Xa inhibitors) with appropriate monitoring for that agent. Patients on Arms G and H without a history of a thromboembolic event are required to take a daily aspirin (81 mg or 325 mg) for DVT prophylaxis. Patients who are unable to tolerate aspirin should receive low molecular weight heparin therapy or warfarin treatment or another accepted full anticoagulation regimen. Ways to minimize risk of DVT should be discussed with patients, including, but not limited to, avoiding smoking, minimizing prothrombotic hormone replacement, avoiding prolonged periods of inactivity (e.g. uninterrupted long car or plane trips). * HIV-positive patients are not excluded but, to enroll, must meet all of the below criteria: * HIV is sensitive to antiretroviral therapy * Must be willing to take effective antiretroviral therapy, if indicated * CD4 count at screening \>= 300 cells/mm³ * If on antiretroviral therapy, must not be taking zidovudine or stavudine * Must be willing to take prophylaxis for Pneumocystis jiroveci pneumonia (PCP) during therapy and until at least 2 months following the completion of therapy or until the CD4 cells recover to over 250 cells/mm³, whichever occurs later Step 1 (Induction) Exclusion Criteria: * Women (sexually mature female) must not be pregnant or breast-feeding * Evidence of prior malignancy except adequately treated non-melanoma skin cancer, in situ cervical carcinoma, low grade prostate carcinoma (Gleason grade ≤ 6) managed with observation that has been stable for at least 6 months, or any malignancy treated with curative intent continuously disease free for \>=3 years so as not to interfere with interpretation of radiographic response * Prior therapy for MCL, except: \< 2 weeks of steroid therapy for symptom control or local radiation therapy for symptom control if there is measurable disease outside the radiation portal. Patients may be on chronic steroids for non-malignant disease if on a stable dose equivalent to ≤ 20 mg prednisone per day. * CNS involvement * History of AIDS-defining conditions * Grade 2 or greater peripheral neuropathy. * NYHA Class III or IV heart failure, uncontrolled angina severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia * Hypersensitivity to bortezomib, boron or mannitol * A serious medical or psychiatric illness likely to interfere with study participation * Participating in any other therapeutic clinical trial or taking any other experimental medications within 14 days prior to registration. Step 2 (Maintenance) Inclusion Criteria: * ECOG performance status between 0-2 * Complete response, partial response or stable disease after Step 1 * ANC \>= 1000 cells/mm3 (1.0 x 10\^9/L) * Platelets \>= 75,000 cells/mm3 (75 x 10\^9/L) * AST/ALT \<= 2 x upper limit of normal (ULN) * Total bilirubin \<= 2 x upper limit of normal (ULN) or, if total elevated, direct bilirubin \<= 2 x upper limit of normal (ULN) * Calculated creatinine clearance by Cockroft-Gault formula \>= 30 ml/min * Patient agrees that if randomized to Arms C or D, and proceeding onto Arms G or H, they must register into the mandatory REMS program, and be willing and able to comply with the requirements of REMS. * Pregnancy tests must occur within 10 - 14 days and again within 24 hours prior to initiation of Cycle 1 of lenalidomide. * Females of childbearing potential (FCBP)\* with regular or no menstruation must have a pregnancy test weekly for the first 28 days and then every 28 days while on lenalidomide therapy (including breaks in therapy); at discontinuation of lenalidomide and at Day 28 post the last dose of lenalidomide. Females with irregular menstruation must have a pregnancy test weekly for the first 28 days and then every 14 days while on lenalidomide therapy (including breaks in therapy), at discontinuation of lenalidomide and at Day 14 and Day 28 post the last dose of lenalidomide (see Appendix VI: Risks of Fetal Exposure, Pregnancy Testing Guidelines and Acceptable Birth Control Methods). * Females of childbearing potential (FCBP)\* must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 10 - 14 days and again within 24 hours prior to starting Cycle 1 of 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 28 days 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 FCBP even if they have had a successful vasectomy. All patients must be counseled at a minimum of every 28 days about pregnancy precautions and risks of fetal exposure. * A female of childbearing potential is any sexually mature female, regardless of sexual orientation of whether they have undergone tubal ligation, who meets the following criteria: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months). * Females of childbearing potential (FCBP) must agree to use two reliable forms of contraception simultaneously or to practice complete abstinence from heterosexual intercourse during the following time periods related to this study/lenaliomide: 1) for at least 28 days before starting lenalidomide; 2) while participating in the study including interruptions in therapy; and 3) for at least 28 days after discontinuation/stopping lenalidomide. The two methods of reliable contraception must include one highly effective method (i.e. intrauterine device (IUD), hormonal \[birth control pills, injections, or implants\], tubal ligation, partner's vasectomy) and one additional effective (barrier) method (i.e. latex condom, diaphragm, cervical cap). FCBP must be referred to a qualified provider of contraceptive methods if needed. * Women must agree to abstain from donating blood during study participation and for at least 28 days after discontinuation from protocol treatment. * Males must agree to abstain from donating blood, semen, or sperm during study participation and for at least 28 days after discontinuation from protocol treatment. All males, regardless of whether they have undergone a successful vasectomy, must agree to use a latex condom during sexual contact with a female of childbearing potential, or to practice complete abstinence from heterosexual intercourse with any female of childbearing potential during all cycles of study treatment and for at least 28 days following discontinuation of protocol treatment * Patients must have no medical contra-indications to, and be willing to take, DVT prophylaxis as all patients registering to the lenalidomide/rituximab Arms G and H will be required to have deep vein thrombosis (DVT) prophylaxis. Patients randomized to Arms G or H who have full anticoagulation, a history of a thrombotic vascular event will be required to have therapeutic doses of low molecular weight heparin or warfarin to maintain an INR between 2.0 - 3.0, or any other accepted full anticoagulation regimen (e.g. direct thrombin inhibitors or Factor Xa inhibitors) with appropriate monitoring for that agent. Patients on Arms G and H without a history of a thromboembolic event are required to take a daily aspirin (81 mg or 325 mg) for DVT prophylaxis. Patients who are unable to tolerate aspirin should receive low molecular weight heparin therapy or warfarin treatment or another accepted full anticoagulation regimen. Ways to minimize risk of DVT should be discussed with patients, including, but not limited to, avoiding smoking, minimizing pro-thrombotic hormone replacement, avoiding prolonged periods of inactivity (e.g. uninterrupted long car or plane trips).