Inclusion Criteria:  Participants must meet the following criteria on screening examination to be eligible to participate in the study:  Participants must have histologically determined mantle cell lymphoma with pathologic review at the participating institutions, that has either:  Relapsed or primary refractory after at least one line of therapy including anti-CD20 monoclonal antibody treatment (part A) or; Had no previous anti-lymphoma therapy other than corticosteroids or radiotherapy (part B). Participants in part A, relapsed or refractory following prior therapy, may have had a prior autologous or allogeneic stem cell transplant and may have been treated with chimeric antigen receptor T-cells (CAR T-cells).  Participants in part B, without prior anti-lymphoma therapy, must require treatment as defined by any of the following criteria:  Symptomatic adenopathy or splenomegaly Local symptoms due to extranodal disease Organ function impairment due to disease involvement, including cytopenias due to marrow involvement (WBC <1.5x109/L; absolute neutrophil count [ANC] <1.0x109/L, Hgb <10g/dL; platelets <100x109/L) Presence of systemic B symptoms (fever, drenching night sweats, or unintentional weight loss ≥ 10% body weight over previous 6 months) or functionally significant fatigue Participants in part B without prior anti-lymphoma therapy should be deemed to be ineligible for autologous stem cell transplant by the treating physician and/or have a TP53 mutation detected by next generation sequencing at a variant (mutant) allele fraction above the validated threshold for calling a new variant Participants in part B must have an archived formalin-fixed paraffin-embedded (FFPE) tumor tissue specimen from the original diagnostic biopsy and peripheral blood available for submission to Adaptive Biotechnologies for ClonoSEQ®ID molecular marker identification of a unique clonal immunoglobulin DNA sequence. Only those participants in part B who have a molecular marker identified from the peripheral blood will be eligible for minimal residual disease (MRD) driven treatment interruptions. Participants in part B who do not have a molecular marker identified by ClonoSEQ from the peripheral blood will be deemed to be MRD indeterminate and are not eligible for peripheral blood MRD driven treatment interruptions. These participants will be able to enroll in the study assuming all other eligibility criteria are met but will receive 7 cycles of AVO combination therapy followed by 17 cycles of acalabrutinib and venetoclax therapy (24 total cycles of AV) and 2 years of maintenance obinutuzumab for a total of 31 cycles of therapy. Measurable disease with a lymph node or tumor mass ≥ 1.5 cm in at least one dimension by CT, PET/CT, or MRI. Patients without measurable disease will be eligible if they have marrow involvement and cytopenias related to their lymphoma (hemoglobin <10 g/dL, absolute neutrophil count < 1.0 x 109/L, or platelets < 100 x 109/L) OR symptomatic splenomegaly > 15cm in craniocaudal diameter. Age ≥ 18 years. ECOG performance status ≤2 (Karnofsky ≥60%)  Participants in parts A and B must have adequate organ and marrow function as defined below:  Absolute neutrophil count ≥ 750 cells/mm3 (0.75 x109/L) unless due to marrow involvement by lymphoma in which case ANC must be ≥ 500 cells/mm3 (0.5x109/L) Platelet count without transfusional support must be ≥ 75,000 cells/mm3 (75 x109/L), unless due to marrow involvement by lymphoma, in which case platelets must be ≥ 50,000 cells/mm3 (50 x109/L) Hemoglobin without transfusional support must be ≥ 8.0 g/dL (80 g/L) unless due to marrow involvement by lymphoma, in which case hemoglobin must be ≥ 7.0 g/dL (70 g/L) Creatinine clearance (CrCl) ≥ 50 ml/min using 24-hour urine collection for creatinine clearance or calculated CrCl or calculated glomerular filtration rate (GFR) ≥ 50 ml/min/1.73 m2 using the CKD-EPI equation Total bilirubin ≤ 2 times the upper limit of normal, unless there is disease involvement of the liver, hemolysis, or a known history of Gilbert's disease, in which case direct bilirubin must be ≤ 3 times the upper limit of normal AST and ALT ≤ 2.5 times the upper limit of normal, unless documented liver involvement by lymphoma, in which case AST and ALT must be ≤ 5 times the upper limit of normal PT/INR ≤ 2 times the upper limit of normal and PTT ≤ 2 times the upper limit of normal Willingness to provide pre-treatment bone marrow (or recent archival w/o intervening therapy) and on-treatment bone marrow and peripheral blood samples The effects of the study drugs on the developing human fetus are unknown. Women of child-bearing potential must agree to remain abstinent or use highly effective contraception (defined as contraceptive measures that result in a failure rate of <1% per year) during the treatment period and for at least 2 days after the last dose of acalabrutinib, 90 days after the last dose of venetoclax or 18 months after the last dose of obinutuzumab, whichever is longer. Men with female sexual partners of childbearing potential should agree to remain abstinent or use contraceptive measures which include a condom plus an additional contraceptive method that together result in a failure rate of <1% per year during the treatment period and for at least 90 days after the last dose of venetoclax or 6 months after the last dose of obinutuzumab, whichever is longer. Men should refrain from donating sperm during the same period. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Ability to understand and the willingness to sign a written informed consent document.  Exclusion Criteria:  Participants who exhibit any of the following conditions at screening will not eligible for admission into the study: Participants who have progressed or relapsed after receiving either a BTK inhibitor or BCL2 inhibitor. Participants who are receiving any other investigational agents, or have received investigational agents within 4 weeks (or 3 half-lives, whichever is longer) of beginning treatment.  Concurrent systemic immunosuppressant therapy (e.g., cyclosporine A, tacrolimus, etc., within 28 days of the first dose of study drug or chronic administration of >20 mg/day of prednisone equivalent corticosteroid within 7 days of the first dose)  -- Note: Glucocorticoids for lymphoma symptom palliation are allowed but must be discontinued at time of initiation of protocol therapy.  History of severe allergic reactions attributed to compounds of similar chemical or biologic composition to obinutuzumab, venetoclax, or acalabrutinib. Patients with reactions to other CD20 monoclonal antibodies (e.g. rituximab, ofatumumab) are not excluded if they were able to eventually tolerate treatment in an outpatient setting without grade 2 or higher infusion reactions.  Participants who have a history of other malignancies except:  Malignancy treated with curative intent and with no known active disease present and felt to be at low risk for recurrence by treating physician. Current adjuvant hormonal therapy for disease treated with curative intent is permissible. Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease. Adequately treated carcinoma in situ without evidence of disease. Low-risk prostate cancer on active surveillance Other exceptions may be made after consultation with the study chair Participants with known leptomeningeal or brain metastases. Imaging or spinal fluid analysis to exclude CNS involvement is not required, unless there is clinical suspicion by the treating investigator. Participants who have had a major surgery or significant traumatic injury within 4 weeks of start of study drug, participants who have not adequately recovered from the side effects of any major surgery (defined as requiring general anesthesia), or participants that may require major surgery during the course of the study. Vaccinated with live, attenuated vaccines within 28 days of study entry or need for live virus vaccines at any time during study period. Patients with human immunodeficiency virus (HIV) or active hepatitis C virus (HCV) or hepatitis B virus (HBV) infection. HIV-positive participants are ineligible because of the potential for pharmacokinetic interactions between certain components of anti-retroviral therapy and venetoclax. Patients who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment. Those who are PCR positive will be excluded. Those who are positive for either hepatitis B surface antigen and/or hepatitis B core antibody but negative for HBV DNA will be managed. Patients who are positive for HCV antibody must be negative for HCV by polymerase chain reaction (PCR) to be eligible for study participation. Ongoing or recent infection requiring intravenous antimicrobials at time of screening. Patients with ongoing use of prophylactic antibiotics are eligible as long as there is no evidence of active infection and the antibiotic is not included on the list of prohibited medications. Uncontrolled intercurrent illness or psychiatric illness/social situations that would limit compliance with study requirements, compromise the subject's safety, or put the study outcomes at undue risk. Lactating or pregnant women are excluded from this study because venetoclax has been shown to decrease implantation, litter size, live fetuses, and fetal body weight in animal models. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with venetoclax, breastfeeding should be discontinued if the mother is treated with venetoclax. These potential risks may also apply to other agents used in this study. Known bleeding disorders (e.g. von Willebrand's disease) or hemophilia. Presence of a bleeding gastrointestinal ulcer diagnosed by endoscopy within 3 months prior to enrollment. History of stroke or intracranial hemorrhage within 6 months prior to enrollment. Participants who require warfarin or other vitamin K antagonists for anticoagulation (other anticoagulants are allowed). Currently active, clinically significant cardiovascular disease, such as uncontrolled arrhythmia or Class 3 or 4 congestive heart failure as defined by the New York Heart Association Functional Classification; or a history of myocardial infarction, unstable angina, or acute coronary syndrome within 6 months prior to randomization. Patients with atrial fibrillation are allowed as long as they are adequately rate controlled. Participants who require treatment with proton pump inhibitors. Subjects receiving proton pump inhibitors who switch to H2-receptor antagonists or antacids are eligible for enrollment on this study. Participants who require concurrent treatment with strong CYP3A inhibitors or strong CYP3A inducers are excluded from the study. If patients are receiving strong CYP3A inhibitors/inducers at time of screening but do not require continuous administration of these agents, these patients are eligible if there is a 7-day washout period between discontinuation of the strong CYP3A inhibitor/inducer and initiation of the first study drug, acalabrutinib. Participants who require concurrent treatment with P-gp inhibitors or narrow therapeutic index P-gp substrates are excluded from the study. If patients are receiving P-gp inhibitors or narrow therapeutic index P-gp substrates at time of screening but do not require continuous administration of these agents, these patients are eligible if there is a 7-day washout period between discontinuation of the P-gp inhibitor and initiation of venetoclax. Unable to swallow capsules, a large number of tablets, or malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel if thought by the investigator to compromise systemic absorption, active, symptomatic inflammatory bowel disease or ulcerative colitis, or partial or complete bowel obstruction. Significant co-morbid condition or disease which in the judgment of the Principal Investigator would place the participant at undue risk or interfere with the study.