Ibrutinib Plus Rituximab and Lenalidomide in Treating Elderly Participants With Newly Diagnosed Mantle Cell Lymphoma

Inclusion Criteria: * Confirmed diagnosis of MCL with CD20 and cyclin D1 positivity in tissue biopsy. * Ki-67 \>= 50%. * Patients must have never received any prior systemic therapy for their disease. * Sign (or their legally-acceptable representatives must sign) an informed consent document indicating that they understand the purpose of and procedures required for the study and are willing to participate in the study. * Patients should in general 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) (bone marrow or gastrointestinal \[GI\] only involvement is acceptable). * Eastern Cooperative Oncology Group (ECOG) performance status of 2 or less. * Absolute neutrophil count (ANC) \>= 1000/mm\^3 without transfusion support. * Platelet count \> 100,000/mm\^3. Patients who have bone marrow infiltration by MCL are eligible if their platelet level is \>= 50,000 /mm\^3 independent of platelet transfusions. * Aminotransferase (AST)/serum glutamic oxaloacetic transaminase (SGOT) and aminotransferase (ALT)/serum glutamic pyruvic transaminase (SGPT) =\< 3 x upper limit of normal. * Serum bilirubin \< 1.5 mg/dl unless bilirubin rise is due to Gilbert's syndrome or of non-hepatic origin. * Creatinine (Cr) clearance \>= 25 mL/min (per Cockcroft-Gault equation). * Disease free of prior malignancies of equal to or greater than 6 months 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, with a life expectancy \> 3 years. * Patients must be willing to receive transfusions of blood products. * Willing and able to participate in all study related procedures and therapy including swallowing capsules without difficulty. * Men must agree 1) to use a latex condom during sexual contact with a female of childbearing potential (FCBP) even if they have had a vasectomy from the time of signing the informed consent form through 90 days after the last dose of lenalidomide and ibrutinib; 2) to not donate sperm during and after the study. Females of childbearing potential (FCBP) 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 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 through 90 days and ibrutinib through 30 days after the last dose of study drug. FCBP must also agree to ongoing pregnancy testing. * All patients must be registered in and must comply with all requirements of the Revlimid Rems program. Exclusion Criteria: * Any serious medical condition that, in the investigator opinion, places the patient at unacceptable risk and/or would prevent the subject from signing the informed consent form. Examples include but are not limited to, uncontrolled hypertension, uncontrolled diabetes mellitus, active/symptomatic coronary artery disease, active infection requiring treatment with intravenous (IV) antibiotics, antiviral or antifungal agents, active hemorrhage, or psychiatric illness in the investigator's opinion places the patient at unacceptable risk and would prevent the subject from signing the informed consent form. * Pregnant or breastfeeding females. * Known human immunodeficiency virus (HIV) infection. Patients with active hepatitis B infection (not including patients with prior hepatitis B vaccination; or positive serum hepatitis B antibody). Known hepatitis C infection is allowed as long as there is no active disease. These patients should be optimized by GI consultation for hepatitis B and infectious disease consult for hepatitis C. * The patient has a prior or concurrent malignancy that in the opinion of the investigator, presents a greater risk to the patient's health and survival, than of the MCL, within the subsequent 6 months at the time of consent. * History of stroke or intracranial hemorrhage within 6 months prior to signing the consent. * Patients at high-risk for thromboembolic disease, such as those with prior heterotopic ossification (h/o) deep venous thrombosis (DVT). * Clinically significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure or myocardial infarction within 6 months at the time of consent or any class 3 (moderate) or 4 (severe) cardiac disease defined by the New York Heart Association classification. * Significant screening electrocardiogram (ECG) abnormalities including left bundle branch block, 2nd degree atrioventricular block (AV block) type II, 3rd degree block, bradycardia (\< 50 beats per minute \[bpm\]), or corrected QT (QTc) \> 500 msec. * Patients with persistent and uncontrolled atrial fibrillation even if rate controlled. * 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. * Major surgery or wound that has not fully healed within 4 weeks or vaccination with live attenuated vaccines within 4 weeks of the first dose of study drugs. * Requires concomitant anticoagulation with warfarin or equivalent vitamin K antagonist. * Requires treatment with strong cytochrome P4503A (CYP3A) inhibitors. * All patients with central nervous system lymphoma.