Bortezomib, Rituximab and Combination Chemotherapy in Treating Participants With Mantle Cell Lymphoma

Inclusion Criteria: * Confirmed diagnosis of previously untreated nodular or diffuse mantle cell lymphoma and their blastoid cytologic variant. * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2. * Serum bilirubin \< 1.5 mg/dl and serum creatinine \< 2.0 mg/dl within 14 days before enrollment (unless higher levels are due to lymphoma). * Platelet count \> 100,000/mm\^3 within 14 days before enrollment (unless due to lymphoma). * Absolute neutrophil count (ANC) \> 1,000/mm\^3 within 14 days before enrollment (unless due to lymphoma). * Cardiac ejection fraction \>= 50% by echocardiogram (ECHO) or multigated acquisition (MUGA). * Patients must be willing to receive transfusions of blood products. * Voluntary written Institutional Review Board (IRB)-approved informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care. * Female subject is either post-menopausal for at least 1 year before the Screening visit or surgically sterilized or if they are of childbearing potential, agree to practice 2 effective methods of birth control, at the same time (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) from the time of signing the informed consent through 30 days after the last dose of study treatment, or agree to completely abstain from heterosexual intercourse. * Male subject, even if surgically sterilized (ie, status post vasectomy) agrees to practice effective barrier contraception during the entire study treatment period and through 30 days after the last dose of study treatment, or agree to completely abstain from heterosexual intercourse. Exclusion Criteria: * Human immunodeficiency virus (HIV) infection. * Central nervous system (CNS) involvement. * Co-morbid medical or psychiatric illnesses that preclude treatment with intense dose chemotherapy. * Concurrent or previous malignancy with \< 90% probability of survival at 5 years. * Patient has \>= grade 2 peripheral neuropathy within 14 days before enrollment. * Myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. Prior to study entry, any electrocardiography (ECG) abnormality at screening has to be documented by the investigator as not medically relevant. * Patient has hypersensitivity to bortezomib, boron or mannitol. * Female subject is pregnant or breast-feeding. Confirmation that the subject is not pregnant must be established by a negative serum B-human chorionic gonadotropin (B-hCG) pregnancy test result obtained during screening. Pregnancy testing is not required for post-menopausal or surgically sterilized women. * Participating in clinical trials with other investigational agents not included in this trial within 14 days of the start of this trial and throughout the duration of this trial. * Radiation therapy within 3 weeks before randomization. Enrollment of subjects who require concurrent radiotherapy (which must be localized in its field size) should be deferred until the radiotherapy is completed and 3 weeks have elapsed since the last date of therapy.