Acalabrutinib, Umbralisib, and Ublituximab for the Treatment of Previously Untreated Mantle Cell Lymphoma

Inclusion Criteria:

* Documented informed consent of the participant and/or legally authorized representative

  * Assent, when appropriate, will be obtained per institutional guidelines
* Histologically confirmed mantle cell lymphoma with documentation of monoclonal CD20+ B cells that have a chromosome translocation t(11;14)(q13;q32) and/or overexpress cyclin D1
* Age \>= 65 years; or \>= 50 years and deemed ineligible for aggressive induction therapy or autologous stem cell transplant by the investigator, or unwilling to undergo aggressive induction; or \>= 18 years with documented del(17p), or TP53 mutation, or complex karyotype (CK) by cytogenetics and/or fluorescence in situ hybridization (FISH) studies
* Requiring treatment for MCL, and for which no prior systemic anticancer therapies have been received (local radiotherapy not exceeding a total dose of 20 Gy at least 2 weeks prior the first dose of study therapy is allowed)
* Measurable disease by computed tomography (CT) or positron emission tomography (PET)/CT scan with one or more sites of disease \>= 1.5 cm in longest dimension (including splenomegaly), or bone marrow involvement with or without malignant lymphocytosis
* Without bone marrow involvement: Absolute neutrophil count (ANC) \>= 1000/mm\^3

  * NOTE: Growth factor is not permitted within 7 days of ANC assessment unless cytopenia is secondary to disease involvement
* With bone marrow involvement: ANC \>= 500/mm\^3

  * NOTE: Growth factor is not permitted within 7 days of ANC assessment unless cytopenia is secondary to disease involvement
* Without bone marrow involvement: Platelets \>= 75,000/mm\^3

  * NOTE: Platelet transfusions are not permitted within 7 days of platelet assessment unless cytopenia is secondary to disease involvement
* With bone marrow involvement: Platelets \>= 30,000/mm\^3

  * NOTE: Platelet transfusions are not permitted within 7 days of platelet assessment unless cytopenia is secondary to disease involvement
* Total bilirubin =\< 1.5 X upper limit of normal (ULN) or =\< 3X ULN for Gilbert's disease
* Aspartate aminotransferase (AST) =\< 2.5 x ULN
* Alanine aminotransferase (ALT) =\< 2.5 x ULN
* Creatinine clearance of \>= 30 mL/min per 24 hour urine test or the Cockcroft-Gault formula
* If not receiving anticoagulants: International normalized ratio (INR) OR prothrombin (PT) =\< 1.5 x ULN. If on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants
* If not receiving anticoagulants: Activated partial thromboplastin time (aPTT) =\< 1.5 x ULN. If on anticoagulant therapy: aPTT must be within therapeutic range of intended use of anticoagulants
* Left ventricular ejection fraction (LVEF) \>= 40%
* Women of childbearing potential (WOCBP): negative serum pregnancy test
* Agreement by females and males of childbearing potential to use an highly effective method of birth control or abstain from heterosexual activity for the course of the study through at least 2 days after the last dose of acalabrutinib for females, and at least 4 months after the last dose of ublituximab or umbralisib, whichever comes later, for both men and women

  * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only)

Exclusion Criteria:

* Chronic use of corticosteroids \>= 20 mg/day (short-term use of steroids \< 14 days is allowed)
* Major surgical procedure within 28 days of start of protocol therapy. 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
* Known history of hypersensitivity or anaphylaxis to study drug(s) including active product or excipient components
* Concurrent participation in another therapeutic clinical trial
* Subjects for whom the goal of therapy is tumor debulking before stem cell transplant
* History of prior malignancy. Exceptions include malignancy treated with curative intent and no known active disease present for \>= 2 years prior to initiation of protocol therapy; adequately treated non-melanoma skin cancer or lentigo maligna (melanoma in situ) without evidence of disease; adequately treated in situ carcinomas (e.g., cervical, esophageal, etc.) without evidence of disease; asymptomatic prostate cancer managed with "watch and wait" strategy
* Uncontrolled AIHA (autoimmune hemolytic anemia) or ITP (idiopathic thrombocytopenic purpura)
* 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
* Requires treatment with a strong cytochrome P450 3A4 (CYP3A4) inhibitor/inducer
* Requires or receiving anticoagulation with warfarin or equivalent vitamin K antagonists
* 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
* Presence of a gastrointestinal ulcer diagnosed by endoscopy within 3 months before screening
* Known bleeding disorders (e.g., von Willebrand's disease or hemophilia)
* History of significant cerebrovascular disease/event, including stroke, myocardial infarction or intracranial hemorrhage, within 6 months prior to start of protocol therapy
* Known active central nervous system (CNS) involvement by lymphoma, including leptomeningeal involvement
* Clinically significant cardiovascular disease such as symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of screening, or any class III or IV cardiac disease as defined by the New York Heart Association Functional Classification. Note: Subjects with controlled, asymptomatic atrial fibrillation can enroll on study
* Unstable angina (angina symptoms at rest), new-onset angina (begun within the last 6 months)
* History of or current progressive multifocal leukoencephalopathy (PML)
* Inability to swallow and retain an oral medication
* Clinically significant uncontrolled illness, including active infection requiring antibiotics
* Live virus vaccines within 4 weeks of start of protocol therapy or planned administration of live virus vaccines during ublituximab therapy
* Evidence of chronic active hepatitis B (HBV, not including patients with prior hepatitis B vaccination; or positive serum Hepatitis B antibody) or chronic active hepatitis C infection (HCV), or active cytomegalovirus (CMV). If hepatitis B virus core (HBc) antibody is positive, the subject must be evaluated for the presence of HBV deoxyribonucleic acid (DNA) by polymerase chain reaction (PCR). If HCV antibody is positive, the subject must be evaluated for the presence of HCV RNA by PCR. If the subject is CMV IgG or CMV IgM positive, the subject must be evaluated for the presence of CMV DNA by PCR. Subjects with positive HBc antibody and negative HBV DNA by PCR are eligible. Subjects with positive HCV antibody and negative HCV RNA by PCR are eligible. Subjects who are CMV IgG or CMV IgM positive but who are CMV DNA negative by PCR are eligible. Patients with a prior known history of hepatitis B and those with a positive anti-HBc with negative hepatitis B surface antigen (HBsAg) at screening must be able to receive antiviral agents effective against hepatitis B
* Known history of human immunodeficiency virus (HIV) infection
* Females only: Pregnant or breastfeeding
* Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures
* Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)