Modified VR-CAP and Acalabrutinib as First Line Therapy for the Treatment of Transplant-Eligible Patients With Mantle Cell Lymphoma

Inclusion Criteria:

* Age 18-75 years
* No prior therapy for mantle cell lymphoma (MCL)
* MCL in need of systemic therapy, and potentially eligible for ASCT as assessed by the treating physician
* Documented histological confirmation of MCL by local institutional review
* Documented, fludeoxyglucose F-18 (FDG)-avid measurable disease (at least 1 lesion \>= 1.5 cm in diameter) as detected by positron emission tomography (PET)/computed tomography (CT) and as defined and includes measurable nodal and extranodal disease sites, or splenomegaly measuring more than 13 cm in vertical length
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, 2
* Absolute neutrophil count (ANC) \>= 1000/mm\^3 or \>= 500/mm\^3 if due to lymphomatous marrow or spleen involvement (obtained =\< 30 days prior to registration)
* Platelet count \>= 100,000/mm\^3 or \>= 75,000/mm\^3 if due to lymphomatous marrow or spleen involvement (obtained =\< 30 days prior to registration)
* Total bilirubin =\< 1.5 x upper limit of normal (ULN) (unless documented Gilbert's syndrome, for which total bilirubin =\< 3 x upper limit of normal \[ULN\] is permitted) (obtained =\< 30 days prior to registration)
* Aspartate transaminase (AST) =\< 3 x ULN (obtained =\< 30 days prior to registration)
* Prothrombin time (PT)/international normalized ratio (INR) or partial thromboplastin time (PTT) =\< 2 x ULN, unless elevated due to a lupus anticoagulant (obtained =\< 30 days prior to registration)
* Calculated creatinine clearance must be \>= 30 ml/min using the Cockcroft-Gault formula (obtained =\< 30 days prior to registration)
* Negative pregnancy test done within =\< 14 days prior to registration for women of childbearing potential only
* For women of childbearing potential (WOCBP, defined as premenopausal women capable of becoming pregnant): Must agree to use of highly effective method of birth control during study therapy and until 12 months after last dose of study therapy. NOTE: 'Acceptable' methods are not adequate. Highly effective methods are defined by Clinical Trials Facilitation and Coordination Group \[CTFG\] as having a failure rate of \< 1% per year
* Men must agree to use barrier contraception starting with the first dose of study therapy and through 180 days after completion of study therapy
* Provide informed written consent
* Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study)
* Hematologic labs must be obtained within =\< 14 days of registration
* Willing and able to participate in all required evaluations and procedures in this study protocol
* Ability to understand the purpose and risks of the study and provide signed and dated informed consent and authorization to use protected health information

Exclusion Criteria:

* Prior systemic treatment for mantle cell lymphoma. Short course of steroids (=\< 7 days) for symptom management or localized radiation is permissible, as long as measurable disease outside of the radiation field exists
* Peripheral neuropathy or neuropathic pain of grade 2 or worse as assessed by the investigator
* Prior exposure to bortezomib or a BTK inhibitor
* Prior anthracycline exposure unless cumulative prior exposure is under 150 mg per square meter
* Requiring anticoagulation with warfarin or equivalent vitamin k antagonist
* Uncontrolled AIHA (autoimmune hemolytic anemia) or ITP (idiopathic thrombocytopenia purpura)
* Active bleeding or history of bleeding diathesis (e.g. hemophilia or von Willebrand disease)
* History of stroke or intracranial hemorrhage within 6 months prior to enrollment
* Requires treatment with a strong cytochrome P450 3A4 (CYP3A4) inhibitor/inducer
* Requiring treatment with a proton pump inhibitor. Examples include: dexlansoprazole, esomeprazole, lansoprazole, omeprazole, pantoprazole, rabeprazole, or therapeutic class equivalents

  * Note: H2-receptor agonists are not exclusionary
* History of allergic reactions attributed to acalabrutinib, cytarabine, bortezomib, boron, or any of the other agents administered as part of the therapeutic regimen in this study
* Active systemic fungal, bacterial, viral, or other infection that is worsening (defined as increasing signs/symptoms of infection during screening) or, requires intravenous antibiotic therapy
* Active or chronic uncontrolled hepatitis B or hepatitis C infection. Patients with positive hepatitis B core antibody positive require negative polymerase chain reaction (PCR) prior to enrollment. Hepatitis B surface antigen positive or PCR positive patients will be excluded. Patients with hepatitis C must have negative hepatitis C virus (HCV) ribonucleic acid (RNA) for inclusion
* Co-morbid systemic illnesses or other severe concurrent disease (including major surgery within 2 weeks) which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens
* Known to be human immunodeficiency virus (HIV) positive since antiretroviral therapy has a potential for drug interactions with acalabrutinib
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure or low cardiac ejection fraction (New York Heart Association \[NYHA\] class 3-4 or ejection fraction \[EF\] \< 45%), unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm
* Other active malignancy =\< 2 years prior to registration. EXCEPTIONS: Non-melanotic skin cancer localized prostate cancer, or carcinoma-in-situ of the breast or cervix. NOTE: If there is a history or prior malignancy, patients must not be receiving other specific treatment for their cancer
* Pregnant and/or breastfeeding
* Has difficulty with or is unable to swallow oral medication, or has significant gastrointestinal disease that would limit absorption of oral medication
* Presence of a gastrointestinal ulcer diagnosed by endoscopy within 3 months before screening. unless directly due to MCL Involvement by endoscopic or histologic evaluation
* Major surgical procedure within 28 days of first dose of study drug. NOTE: If a subject had major surgery, they must have recovered adequately from any toxicity and/or complications from the intervention before the first dose of study drug
* Concurrent participation in another therapeutic clinical trial