Acalabrutinib in Combination With Venetoclax or Obinutuzumab for the Treatment of Treatment-naive Chronic Lymphocytic Leukemia

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