Ibrutinib, Rituximab, Venetoclax, and Combination Chemotherapy in Treating Patients With Newly Diagnosed Mantle Cell Lymphoma

Inclusion Criteria:

* Confirmed diagnosis of mantle cell lymphoma with CD20 positivity in tissue biopsy
* MCL patients must have a clinical indication to start systemic therapy. Symptoms and features of MCL include any of the following: a) B-symptoms, b) Mantle Cell Lymphoma International Prognostic Index (MIPI) \> 3, c) Ki 67 \>= 30%, d) bulky tumors \> 10 cm or in case of \>= 2 tumors, each \>= 5 cm in diameter, e) disease threatening organ function, f) elevated lactate dehydrogenase (LDH), g) peripheral blood (PB) white blood cell (WBC) \> 50,000, h) pancytopenia due to bone marrow MCL, i) patient's choice due to anxiety; j) pain due to lymphoma; k) somatic mutations in the TP53, NSD2 or NOTCH genes; l) size of spleen \>= 20 cm
* Newly diagnosed MCL with no prior therapy
* 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, including biomarkers, and are willing to participate in the study
* Bi-dimensional measurable disease using both computed tomography (CT) scan and/or positron emission tomography (PET)-CT or gastrointestinal biopsies, CT gastrointestinal, bone marrow or spleen only patients are allowable
* Eastern Cooperative Oncology Group (ECOG) performance status of 2 or less
* Absolute neutrophil count (ANC) \>= 1000/mm\^3 independent of growth factor support
* Platelets \>= 100,000/mm\^3 or \>= 50,000/mm\^3 if bone marrow involvement without necessitating transfusion
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x upper limit of normal (ULN)
* Total bilirubin =\< 1.5 x ULN unless bilirubin rise is due to Gilbert's syndrome or of non-hepatic origin
* Creatinine clearance (CLcr) \> 50 mL/min
* Cardiac ejection fraction \>= 50% by echocardiogram (ECHO) or multigated acquisition (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 with life expectancy of greater than 3 years. Principal investigator (PI) can use clinical judgement in the best interest of patients
* Females of childbearing potential (FCBP) must have a negative serum or urine pregnancy test (within 28 days of initiation of protocol therapy) and must be willing to use acceptable methods of birth control during and after the study consistent with local regulations regarding the use of birth control methods for subjects participating in clinical trials. 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. Men must agree to not donate sperm during and after the study. For females, these restrictions apply for 1 month after the last dose of study drug. For males, these restrictions apply for 3 months after the last dose of study drug

  * 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, laboratory abnormality, or psychiatric illness that, in the investigators opinion, places the patient at unacceptable risk or would prevent the subject from signing the informed consent form
* Pregnant or breast-feeding females
* Known human immunodeficiency virus (HIV) infection (HIV testing is not required)
* Evidence of other clinically significant uncontrolled condition(s) including, but not limited to:

  * Uncontrolled and/or active systemic infection (viral, bacterial or fungal)
  * Chronic hepatitis B virus (HBV) or hepatitis C (HCV) requiring treatment. Note: subjects with serologic evidence of prior vaccination to HBV (i.e. hepatitis B surface \[HBs\] antigen negative-, anti-HBs antibody positive and anti-hepatitis B core \[HBc\] antibody negative) or positive anti-HBc antibody from intravenous immunoglobulins (IVIG) may participate
* Treatment with any of the following within 7 days prior to the first dose of study drug:

  * Steroid therapy for anti-neoplastic intent
  * Moderate or strong cytochrome P450 3A (CYP3A) inhibitors
  * Moderate or strong CYP3A inducers
* Administration or consumption of any of the following within 3 days prior to the first dose of study drug:

  * Grapefruit or grapefruit products
  * Seville oranges (including marmalade containing Seville oranges)
  * Star fruit
* 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 and is cleared by gastrointestinal (GI) consultation
* Central nervous system with mantle cell lymphoma
* Significant neuropathy (grades 3 to 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 or a wound that has not fully healed within 4 weeks of randomization. Clearance letter from primary physician required
* Requires anticoagulation with warfarin or equivalent vitamin K antagonist
* Requires chronic treatment with strong CYP3A inhibitors
* Patients with New York Health Association (NYHA) Class III and IV heart failure, myocardial infarction in the preceding 6 months, and significant conduction abnormalities, including but not limited to left bundle branch block, 2nd degree atrioventricular (AV) block type II, 3rd degree block, QT prolongation (corrected QT \[QTc\] \> 500 msec), sick sinus syndrome, ventricular tachycardia, symptomatic bradycardia (heart rate \< 50 bpm), hypotension, light headedness and syncope, persistent and uncontrolled atrial fibrillation
* Recent placement of 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 therapy
* Child-Pugh class B or C are excluded
* Vaccinated with live, attenuated vaccines within 4 weeks of randomization