Acalabrutinib With Bendamustine / Rituximab Followed by Cytarabine / Rituximab for Untreated Mantle Cell Lymphoma

Inclusion Criteria: * Histologically confirmed mantle cell lymphoma with documented expression of Cyclin D1 by immune-histochemical stains and/or t(11;14) by cytogenetics or FISH. * Presence of evaluable disease by PET imaging per the Lugano classification. * Eligible for autologous stem cell transplantation. * Between 18 and 70 years of age, inclusive. * ECOG performance status ≤ 2 * Normal bone marrow and organ function as defined below: * Absolute neutrophil count ≥ 1,000/mcL unless, in the opinion of the treating physician, neutropenia is due to splenomegaly or bone marrow involvement * Platelets ≥ 100,000/mcL unless, in the opinion of the treating physician, thrombocytopenia is due to splenomegaly or bone marrow involvement * Total bilirubin ≤ 2.0 x IULN and AST(SGOT)/ALT(SGPT) ≤ 3.0 x IULN except when, in the opinion of the treating physician, elevation is due to direct involvement of lymphoma (e.g. hepatic infiltration or biliary obstruction due to lymphoma) or Gilbert's disease * Creatinine ≤ IULN OR creatinine clearance ≥ 40 mL/min for patients with creatinine levels above institutional normal * Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately. * Ability to understand and willingness to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable). Exclusion Criteria: * Any previous chemotherapy or radiation for mantle cell lymphoma. Short course of steroids for symptom relief prior to presentation is permissible. * Symptomatic meningeal or parenchymal brain lymphoma. * Prior exposure to a BTK inhibitor. * Currently receiving any other investigational agents. * A history of allergic reactions attributed to compounds of similar chemical or biologic composition to acalabrutinib, rituximab, cytarabine, bendamustine, or other agents used in the study. * Received a live virus vaccination within 28 days of first dose of study drug. * Uncontrolled active systemic fungal, bacterial, viral, or other infection (defined as exhibiting ongoing signs/symptoms related to the infection and without improvement, despite appropriate antibiotics or other treatment), or intravenous anti-infective treatment within 2 weeks before first dose of study drug. * Clinically significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of screening, or any Class 3 or 4 cardiac disease as defined by the New York Heart Association Functional Classification, or corrected QT interval (QTc) \> 480 msec at screening. Exception: subjects with controlled, asymptomatic atrial fibrillation during screening are allowed to enroll on study. * Malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel that is likely to affect absorption, symptomatic inflammatory bowel disease, partial or complete bowel obstruction, or gastric restrictions and bariatric surgery, such as gastric bypass. * Active bleeding or history of bleeding diathesis (eg, hemophilia or von Willebrand disease). * Uncontrolled AIHA (autoimmune hemolytic anemia) or ITP (idiopathic thrombocytopenic purpura). * Presence of a gastrointestinal ulcer diagnosed by endoscopy within 3 months before screening. * Requires treatment with a strong cytochrome P450 3A4 (CYP3A4) inhibitor/inducer. * Requires or receiving anticoagulation with warfarin or equivalent vitamin K antagonists (e.g., phenprocoumon) within 7 days of first dose of study drug. * Prothrombin time (PT)/INR or aPTT (in the absence of lupus anticoagulant) \>2x ULN. Exception: Subjects receiving warfarin are excluded; however, those receiving other anticoagulant therapy who have a higher INR/aPTT may be permitted to enroll to this study after discussion with the PI. * Requires treatment with proton pump inhibitors (e.g., omeprazole, esomeprazole, lansoprazole, dexlansoprazole, rabeprazole, or pantoprazole). Subjects receiving proton pump inhibitors who switch to H2-receptor antagonists or antacids are eligible for enrollment to this study. * History of significant cerebrovascular disease/event, including stroke or intracranial hemorrhage, within 6 months before the first dose of study drug. * 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. * Subjects with serologic status reflecting active viral hepatitis B or C infection. Subjects who are hepatitis B core antibody positive but surface antigen negative will need negative polymerase chain reaction (PCR) prior to enrollment. Hepatitis B surface antigen positive or PCR positive patients will be excluded. Subjects who are hepatitis C antibody positive will need negative PCR prior to enrollment. Subjects with positive hepatitis C PCR will be excluded. * Pregnant and/or breastfeeding. Women of childbearing potential must have a negative serum pregnancy test within 14 days of study entry. * Known HIV-positivity on combination antiretroviral therapy because of the potential for pharmacokinetic interactions with acalabrutinib. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy