Acalabrutinib with Venetoclax or Obinutuzumab for CLL

Inclusion Criteria: * Men and women \>= 18 years of age * Diagnosis of CLL/small lymphocytic lymphoma (SLL) meeting criteria established in the 2018 International Workshop (iw)CLL guidelines * Must be treatment-naive: Received no prior chemotherapy, immunotherapy, or targeted therapy for the treatment of CLL, with the exceptions of palliative loco-regional radiotherapy, rituximab for autoimmune conditions, or corticosteroids for symptoms control * Patients must meet criteria for treatment as defined by 2018 iwCLL guidelines which includes at least one of the following criteria: * Evidence of marrow failure as manifested by the development or worsening of anemia or thrombocytopenia (not attributable to autoimmune hemolytic anemia or thrombocytopenia) * Massive (\>= 6 cm below the costal margin), progressive or symptomatic splenomegaly * Massive nodes (\>= 10 cm) or progressive or symptomatic lymphadenopathy * Progressive lymphocytosis with a lymphocyte doubling time \< 6 months or an increase of \>= 50% over a 2 month period * Autoimmune anemia and/or thrombocytopenia that is poorly responsive to standard therapy * Symptomatic or functional extranodal involvement (e.g. skin, kidney, lung, spine) * Constitutional symptoms, which include any of the following: * Unintentional weight loss of 10% or more within 6 months * Significant fatigue * Fevers \> 100.5 degrees Fahrenheit (F) for 2 weeks or more without evidence of infection * Night sweats \>= 1 month without evidence of infection * Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 * Adequate bone marrow independent of growth factor support or infusion support at screening unless evidence shows that the cytopenia(s) is due to marrow involvement by CLL/SLL and/or disease-related immune thrombocytopenia, or anemia. If cytopenias are due to disease in the bone marrow any degree of cytopenias are allowed. Patients with active uncontrolled autoimmune cytopenias are excluded * Absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelets \>= 30,000/mm\^3 * Hemoglobin \>= 7 g/dL * Total bilirubin =\< 2.0 x upper limit of normal (ULN) (excepting Gilbert's syndrome) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x ULN * Creatinine clearance \>= 30 mL/min/1.73m\^2 * Using 24-hour creatinine clearance or modified Cockcroft-Gault equation * Woman of childbearing potential (WOCBP) who are sexually active must use highly effective methods of contraception during treatment and for at least 2 days after last acalabrutinib dose, 30 days after last venetoclax dose, and 6 months after last obinutuzumab dose * 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: * Patients with high-risk disease as defined by: * Presence of deletion 17p13 on cytogenetic analysis by fluorescent in situ hybridization (FISH) * Presence of TP53 mutation on next generation sequencing * Presence of complex karyotype on cytogenetic evaluation * Defined as \>= 3 karyotypic abnormalities * Treatment with a moderate or strong CYP3A inhibitor or inducer within 7 days prior to first dose of acalabrutinib or venetoclax or need for treatment with a strong CYP3A inhibitor or inducer during the period or the study. Patients who have a need for treatment with a moderate CYP3A inhibitor or inducer during acalabrutinib or venetoclax dose escalation will also be excluded * Known active involvement of the central nervous system by lymphoma or leukemia * Subject with other malignancies that are associated with a life expectancy of \< 2 years or that would confound assessment of toxicity in this study * Clinically significant cardiovascular disease such as 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. Note: Subjects with controlled atrial fibrillation can enroll on study * Is unable to swallow oral medication, or has significant gastrointestinal disease that would limit absorption of oral medication * Known history of infection with human immunodeficiency virus (HIV) * Subjects with active infections requiring intravenous (IV) antibiotic/antiviral therapy are not eligible for entry onto the study until resolution of the infection. Subjects on prophylactic antibiotics or antivirals are acceptable * Known history of hypersensitivity or anaphylaxis to study drug(s) including active product or excipient components * Active bleeding or history of bleeding diathesis (e.g., hemophilia or von Willebrand disease) * Uncontrolled autoimmune hemolytic anemia (AIHA) or idiopathic thrombocytopenic purpura (ITP) unrelated to underlying CLL * Patients with uncontrolled autoimmune disease requiring \> 20 mg of daily prednisone or equivalent * Presence of a gastrointestinal ulcer diagnosed by endoscopy within 3 months before screening * Requires or receiving anticoagulation with warfarin or equivalent vitamin K antagonists * Prothrombin time (PT)/international normalized ratio (INR) or activated partial thromboplastin time (aPTT) (in the absence of lupus anticoagulant) \> 2 x ULN * 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 * Hepatitis B or C serologic status: * Subjects who are hepatitis B core antibody (anti-HBc) positive and who are hepatitis B surface antigen (HBsAg) negative will need to have a negative polymerase chain reaction (PCR) and must be willing to undergo deoxyribonucleic acid (DNA) PCR testing during the study to be eligible. Those who are HBsAg positive or hepatitis B PCR positive will be excluded * Subjects who are hepatitis C antibody positive will need to have a negative PCR result to be eligible. Those who are hepatitis C PCR positive will be excluded * Breastfeeding or pregnant * Vaccination with live vaccines 28 days prior to registration for study screening * Concurrent participation in another therapeutic clinical trial