Ibrutinib, Rituximab, and Consolidation Chemotherapy in Treating Young Patients With Newly Diagnosed Mantle Cell Lymphoma

Inclusion Criteria: * Patient has a confirmed diagnosis of mantle cell lymphoma with CD20 positivity in tissue biopsy * Patients with MCL must be symptomatic and need immediate therapy; symptoms and nature of MCL include any of the following: * Blastoid variant * Pleomorphic variant * B symptoms * Mantle Cell International Prognostic Score (MIPI) \> 3 * Ki-67 \>= 30% * Bulky tumors \> 7 cm or in case of \>= 2 tumors, each \>= 5 cm in diameter * Disease threatening organ function * Elevated lactate dehydrogenase (LDH) * Peripheral blood white blood cell (PB WBC) \> 50,000 * Pancytopenia due to bone marrow MCL * Patient's choice due to anxiety * Pain due to lymphoma * Somatic mutations in the TP53, c-MYC or NOTCH genes * Size of spleen \>= 20 cm * Patients with mantle cell lymphoma with any of the following will be considered "high-risk" for the purpose of this protocol: * Blastoid or pleomorphic histology * Ki-67 index larger than 30% * Bulky tumor of larger than 7 cm or in case of multiple tumors, larger than or equal to 5 cm each in diameter * Somatic mutations in the TP53, c-MYC or NOTCH genes * Size of spleen \>= 20 cm * Patient has newly diagnosed disease with no prior therapy * Understand and voluntarily sign an Institutional Review Board (IRB)-approved informed consent form * Age =\< 65 years at the time of signing the informed consent * Patients should have bi-dimensional measurable disease using the Cheson criteria (measurable disease by computed tomography \[CT\] scan defined as at least 1 lesion that measures \>= 1.5 cm in single dimension) * Gastrointestinal or bone marrow or spleen only patients are allowable * Eastern Cooperative Oncology Group (ECOG) performance status of 2 or less * An absolute neutrophil count (ANC) \> 1,000/mm\^3 (patients who have bone marrow infiltration by MCL are eligible if their ANC is \>= 500/mm\^3 \[growth factor allowed\]; these patients should be discussed with either the principal investigator \[PI\] or Co-PI of the study for final approval) * Platelet count \> 100,000/mm\^3 (patients who have bone marrow infiltration by MCL are eligible if their platelet level is equal to or \> than 20,000/mm\^3; these patients should be discussed with either the PI or Co-PI of the study for final approval) * Serum bilirubin \< 1.5 mg/dl * Creatinine (Cr) clearance \>= 30 mL/min * Aspartate transaminase (AST)/serum glutamic oxaloacetic transaminase (SGOT) and alanine transaminase (ALT)/serum glutamic-pyruvate transaminase (SGPT) \< 2 x upper limit of normal or \< 5 x upper limit of normal if hepatic metastases are present; Gilbert's disease is allowed * Cardiac ejection fraction \>= 50% by echocardiogram (ECHO) or multiple gated acquisition scan (MUGA) * Disease free of prior malignancies with exception of currently treated basal cell, squamous cell carcinoma of the skin, carcinoma "in situ" of the cervix or breast, or other malignancies in remission (including prostate cancer patients in remission from radiation therapy, surgery or brachytherapy), not actively being treated * Females of childbearing potential (FCBP)\* must have a negative serum or urine pregnancy test (within 30 days of initiation of protocol therapy) and must be willing to use acceptable methods of birth control; men must agree to use a latex condom during sexual contact with a female of childbearing potential even if they have had a successful vasectomy * A female of childbearing potential is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) Exclusion Criteria: * Any serious medical condition including but not limited to, uncontrolled hypertension, uncontrolled diabetes mellitus, active/symptomatic coronary artery disease, chronic obstructive pulmonary disease (COPD), renal failure, active hemorrhage, or psychiatric illness that, in the investigators opinion places the patient at unacceptable risk and would prevent the subject from signing the informed consent form * Pregnant or breast feeding females * Known human immunodeficiency virus (HIV) infection * Patients with active hepatitis B or C infection (not including patients with prior hepatitis B vaccination); these patients should be cleared by gastrointestinal (GI) consultation for hepatitis B and infectious disease consult for hepatitis C * All patients with central nervous system lymphoma * Significant neuropathy (grades 3 - 4, or grade 2 with pain) within 14 days prior to enrollment * Contraindication to any of the required concomitant drugs or supportive treatments or intolerance to hydration due to preexisting pulmonary or cardiac impairment including pleural effusion requiring thoracentesis or ascites requiring paracentesis unless due to lymphoma * Malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel or ulcerative colitis, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction, or any other gastrointestinal condition that could interfere with the absorption and metabolism of ibrutinib * Major surgery within 4 weeks of initiation of therapy; clearance letter from primary physician required * Requires anticoagulation with warfarin or equivalent vitamin K antagonist * Requires treatment with strong cytochrome P4503A (CYP3A) inhibitors * Patients with New York Heart Association (NYHA) class III and IV heart failure, myocardial infarction in the preceding 6 months, and significant conduction abnormalities, including but not limited to 2nd degree atrioventricular block (AV block) type II, 3rd degree block, QT prolongation (corrected QT \[QTc\] \> 500 millisecond \[msec\]), sick sinus syndrome, ventricular tachycardia, symptomatic bradycardia (heart rate \< 50 beats per minute \[bpm\]), hypotension, light headedness and syncope; patients with persistent and uncontrolled atrial fibrillation will be excluded; the protocol excludes patients who have recently had a stent and by recommendation of their cardiologist need to stay on anticoagulants such as warfarin or equivalent vitamin K antagonist * Acute infection requiring treatment (IV antibiotics, antivirals, or antifungals) within 14 days prior to initiation of study