Ibrutinib in Treating Participants With Untreated High Risk Smoldering Mantle Cell Lymphoma

Inclusion Criteria: * Confirmed diagnosis of MCL with CD20 and cyclin D1 positivity or cyclin D1 negative MCL classic histology in tissue biopsy. Patients must have never received any prior therapy for their disease. Patients have been observed for 3 - 6 months with no progression as per imaging assessments * High risk smoldering MCL (i.e. patients without any B symptoms or any symptoms related to MCL warranting immediate systemic therapy) with at least one or more of these eligibility criteria: * Ki-67 of 15-30% (Ki-67% from involved tissue not bone marrow \[BM\], unless confirmed by pathologist), * White blood cells (WBC) 15-30k * Lymph node size 3-5 cm in diameter * Complex karyotype * TP53 mutated or wild type and/or del17p (fluorescence in situ hybridization \[FISH\]% 10-50%) * MYC positive MCL. MYC positive (either by FISH or by immunohistochemistry \[IHC\] and confirmed by pathology at MD Anderson Cancer Center \[MDACC\]) * Presence of either or KMT2D, BIRC3, NOTCH2, NSD2 or more than one mutation in the initial next generation sequencing (NGS) panel testing are allowed * Understand and voluntarily sign an institutional review board (IRB)-approved informed consent form * Age \>= 18 years at the time of signing the informed consent * Patients should in general have bi-dimensional measurable disease with their biggest tumor less than or equal to 5 cm. (Bone marrow or gastrointestinal \[GI\] only involvement is acceptable) * Eastern Cooperative Oncology Group (ECOG) performance status of 2 or less * Cardiology clearance is required. Discussion with cardiologist and co-principal investigator (PI) is required before starting ibrutinib * With minimal disease or absent disease related symptoms but anxious to start systemic therapy * Absence of cytopenia attributed to bone marrow (BM) infiltration * Absolute neutrophil count (ANC) \> 1000/mm\^3 * Platelet count \> 100,000/mm\^3 * Patients who have bone marrow infiltration by MCL are eligible if their ANC is \>= than 500 or their platelet level is \>= than 50,000 /mm\^3. Platelet transfusions are allowed * Aspartate aminotransferase (AST)/serum glutamic oxaloacetic transaminase (SGOT) and alanine aminotransferase (ALT)/serum glutamic pyruvic transaminase (SGPT) \< 3 x upper limit of normal or \< 5 x upper limit of normal if hepatic metastases are present * Serum bilirubin \< 1.5 mg/dl * Creatinine (Cr) clearance \>= 30 mL/min * Disease free of prior malignancies for 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. 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 and having a screening core biopsy * Female subjects who are of non-reproductive potential (i.e., post-menopausal by history - no menses for \>= 1 year; OR history of hysterectomy; OR history of bilateral tubal ligation; OR history of bilateral oophorectomy). Female subjects of childbearing potential must have a negative serum pregnancy test upon study entry * Male and female subjects who agree to use highly effective methods of birth control (e.g., implants, injectable, combined oral contraceptives, some intrauterine devices \[IUDs\], sexual abstinence, or sterilized partner) and a barrier method (e.g., condoms, vaginal ring, sponge, etc) during the period of therapy and for 30 days after the last dose of study drug for females and 90 days for males Exclusion Criteria: * Any serious medical condition including but not limited to uncontrolled hypertension, arrhythmias, diabetes mellitus, active/symptomatic coronary artery disease, chronic obstructive pulmonary disease (COPD), renal failure, very painful, intolerable symptoms from splenomegaly, leukemic features, active hemorrhage, or psychiatric illness that, in the investigator's opinion, places the patient at unacceptable risk and would prevent the subject from signing the informed consent form * Patients with ANY of the following risk factors: * Clinically significant disease related symptoms (including significant B symptoms) compromising the performance status to more than 1 * Blastoid variant histology * Pleomorphic variant histology * Ki-67 \> 30% * Bulky tumors \> 5 cm * Central nervous system (CNS) involvement at diagnosis * All patients must not have received any prior treatment for mantle cell lymphoma * Prior exposure to BTK inhibitor * Pregnant or breastfeeding females * Known history of human immunodeficiency virus (HIV) or active with hepatitis C virus (HCV) or hepatitis B virus (HBV). Subjects who are positive for hepatitis B core antibody, hepatitis B surface antigen, or hepatitis C antibody must have a negative polymerase chain reaction (PCR) result before enrollment. Those who are PCR positive will be excluded * All patients with history of central nervous system lymphoma * History of stroke or intracranial hemorrhage within 6 months prior to signing the consent * Currently active, or past history/of clinically significant cardiovascular disease such as uncontrolled arrhythmia or any Class 3 or 4 congestive heart failure as defined by the New York Heart Association Classification, or even controlled arrhythmias (any grade) on medications or a history of myocardial infarction, unstable angina, or acute coronary syndrome within 6 months prior to randomization * Patients with prior history of atrial fibrillation or any type of cardiac arrhythmias and/or who underwent ablation and are in normal sinus rhythm (exceptions include patients who are asymptomatic and those who are given cardiology clearance) * Unable to swallow capsules, 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. * Requires concomitant anticoagulation with warfarin or equivalent vitamin K antagonist, active treatment for pulmonary embolism (PE)/ deep vein thrombosis (DVT) and persons with mechanical cardiac valves * Subject who received a strong cytochrome P450 (CYP) 3A inhibitor within 7 days prior to the first dose of ibrutinib or subject who requires continuous treatment with a strong CYP3A inhibitor * Subjects with chronic liver disease and hepatic impairment meeting Child-Pugh class C * Any uncontrolled active systemic infection * Major surgery within 4 weeks of first dose of study drug * Vaccinated with live, attenuated vaccines within 4 weeks of first dose of study drug * Recent infection requiring systemic treatment that was completed =\< 14 days before the first dose of study drug * Known bleeding disorders (e.g., von Willebrand's disease or hemophilia) * Unresolved toxicities from prior anticancer therapy, defined as having not resolved to Common Terminology Criteria for Adverse Event (CTCAE, version \[v\] 4.0), grade =\< 1, or to the levels dictated in the inclusion/exclusion criteria with the exception of alopecia * Concurrent systemic immunosuppressant therapy within 21 days of the first dose of study drug