Inclusion Criteria:
* PRE-REGISTRATION - INCLUSION CRITERIA
* Age \>= 18 years.
* Confirmed diagnosis of CLL according to the International Workshop on (iw)CLL 2018 criteria or biopsy proven small lymphocytic lymphoma (SLL) according to the World Health Organization (WHO) criteria.
* NOTE: The diagnosis of CLL requires the presence of \> 5 × 10\^9/L B lymphocytes in the peripheral blood. Typically, CLL cells express CD19, CD5, and CD23, with variable expression of CD20 (typically dim), and show kappa or lambda light chain restriction.
* NOTE: A diagnosis of mantle cell lymphoma must be excluded by demonstrating a negative cyclin D1 expression and/or a negative t(11;14) translocation.
* No prior CLL/SLL-directed therapy such as chemotherapy, immunotherapy, targeted therapy with small molecule inhibitors, radiation therapy, or cellular therapy.
* NOTE: Nutraceutical treatments with no established benefit in CLL (such as epigallocatechin gallate or EGCG, found in green tea or other herbal treatments or supplemental vitamins) will not be considered prior CLL/SLL-directed therapy.
* NOTE: Prior corticosteroid therapy for an indication other than CLL/SLL will not be considered prior CLL/SLL-directed therapy.
* NOTE: A short course of corticosteroid (e.g., =\< 1 week of intravenous or =\< 2 weeks of oral corticosteroid) given for acute SLL-related symptoms or impending severe organ dysfunction is allowed.
* Provide written informed consent.
* REGISTRATION - INCLUSION CRITERIA
* Patients with SLL must have a measurable B-cell clone (of CLL immunophenotype) in either peripheral blood or bone marrow (e.g., by flow cytometry) at baseline.
* Meeting at least one of the following indications for treatment:
* Evidence of progressive marrow failure as manifested by the development of, or worsening of, anemia (Hb \< 11 g/dL) and/or thrombocytopenia (platelet counts \< 100 × 10\^9/L).
* Massive (i.e., \>= 6 cm below the left costal margin) or progressive or symptomatic splenomegaly.
* Massive nodes (i.e., \>= 10 cm in longest diameter) or progressive or symptomatic lymphadenopathy.
* Progressive lymphocytosis with an increase of \>= 50% over a 2-month period, or lymphocyte doubling time (LDT) \< 6 months. LDT can be obtained by linear regression extrapolation of absolute lymphocyte counts obtained at intervals of 2 weeks over an observation period of 2 to 3 months; patients with initial blood lymphocyte counts \< 30 × 10\^9/L may require a longer observation period to determine the LDT. Factors contributing to lymphocytosis other than CLL (e.g., infections, steroid administration) should be excluded.
* Autoimmune complications including anemia or thrombocytopenia poorly responsive to corticosteroids.
* Symptomatic or functional extranodal involvement (e.g., skin, kidney, lung, spine).
* Disease-related symptoms as defined by any of the following:
* Unintentional weight loss \>= 10% within the previous 6 months.
* Significant fatigue (i.e., cannot work or unable to perform usual activities).
* Fevers \>= 100.4°F or 38.0°C for 2 or more weeks without evidence of infection.
* Night sweats for \>= 1 month without evidence of infection.
* Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0, 1 or 2
* Absolute neutrophil count (ANC) \>= 0.75 × 10\^9/L (750/mm\^3) (obtained =\< 14 days prior to registration)
* Platelet count \>= 50 × 10\^9/L (obtained =\< 14 days prior to registration)
* Hemoglobin \>= 8 g/dL (obtained =\< 14 days prior to registration)
* Activated partial thromboplastin time (aPTT) or partial thromboplastin time (PTT) and prothrombin (PT) or international normalized ratio (INR) =\< 1.5 × upper normal limit (ULN) (obtained =\< 14 days prior to registration)
* Total bilirubin =\< 1.5 × ULN (or =\< 3 × ULN if there is evidence of parenchymal liver involvement with CLL/SLL); patients with hemolysis or Gilbert's disease may enroll if indirect bilirubin is =\< 3 × ULN and direct bilirubin is =\< 1.5 × ULN (obtained =\< 14 days prior to registration)
* Alanine aminotransferase (ALT) and aspartate transaminase (AST) =\< 3 × ULN (or =\< 5 × ULN if there is evidence of parenchymal liver involvement with CLL/SLL) (obtained =\< 14 days prior to registration)
* Calculated creatinine clearance \>=40 ml/min using the Cockcroft-Gault formula.
* Negative serum pregnancy test done =\< 7 days prior to registration, for persons of childbearing potential only.
* NOTE: Persons of reproductive potential is defined as following: menarche and who are not postmenopausal (and 2 years of non-therapy-induced amenorrhea) or surgically sterile.
* Male and females of reproductive potential must agree to use a highly effective (preferred) or an acceptable form of birth control during study treatment and for 6 months following the last dose of pirtobrutinib.
* Males must be willing to not donate sperm during the study and for 6 months after the last dose of any study drug.
* Willingness to provide mandatory research blood, bone marrow, saliva, and stool specimens for correlative research.
* Willing to return to enrolling institution for follow-up (during treatment and Clinical Follow-up).
Exclusion Criteria:
* REGISTRATION - EXCLUSION CRITERIA
* Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown:
* Pregnant persons.
* Nursing persons (lactating persons are eligible provided that they agree not to breast feed while receiving treatment on the study or within 6 months of the last dose of study treatment).
* Male or females of reproductive potential who are unwilling to employ adequate contraception during treatment and for 6 months after pirtobrutinib.
* Evidence of Richter transformation.
* Central nervous system (CNS) involvement of CLL/SLL (e.g., any parenchymal, leptomeningeal, cerebrospinal fluid \[CSF\], cranial or spinal nerve root involvement).
* Active uncontrolled autoimmune complications (e.g., active autoimmune hemolytic anemia or clinically significant immune thrombocytopenia).
* Receiving any other investigational agent which would be considered as a treatment for the CLL/SLL (with the exception of corticosteroid).
* Any of the following medication requirement or recent use:
* Requirement of a strong cytochrome P450 (CYP) 3A inhibitor or inducer during the study.
* Use of a strong or moderate CYP3A inhibitor or inducer =\< 7 days prior to registration.
* Requirement of a strong P-glycoprotein 1 (PgP) inhibitor during the study.
* Anticoagulation with a vitamin K antagonist =\< 7 days prior to registration or anticipated use during the study.
* Vaccination with live vaccine =\< 28 days prior to registration.
* NOTE: Because of their effect on CYP3A4, use of any of the following =\< 3 days of study therapy start or planned use during study participation is prohibited:
* Grapefruit or grapefruit products.
* Seville oranges or products from Seville oranges.
* Star fruit.
* Malabsorption syndrome or other condition that precludes enteral route of administration.
* History of a bleeding diathesis (e.g., hemophilia, von Willebrand disease, etc.).
* Patients who have tested positive for Human Immunodeficiency Virus (HIV) are excluded due to potential drug-drug interactions between anti-retroviral medications and pirtobrutinib and risk of opportunistic infections with both HIV and irreversible BTK inhibitors. For patients with unknown HIV status, HIV testing will be performed at Screening and result should be negative for enrollment.
* Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens.
* Uncontrolled intercurrent illness including, but not limited to:
* Ongoing or active infection.
* Known active cytomegalovirus (CMV) infection is ineligible; unknown or negative status are eligible.
* Hepatitis B virus (HBV): Patients with positive hepatitis B surface antigen (HBsAg) are excluded. Patients with positive hepatitis B core antibody (anti-HBc) and negative HBsAg require hepatitis B polymerase chain reaction (PCR) evaluation. Patients who are hepatitis B PCR positive will be excluded.
* Hepatitis C virus (HCV): If hepatitis C antibody result is positive, patient will need to have a negative result for hepatitis C ribonucleic acid (RNA). Patients who are hepatitis C RNA positive will be excluded.
* New York Heart Association (NYHA) Class III or IV or symptomatic congestive heart failure.
* Documented left ventricular ejection fraction (LVEF) by any method of =\< 40% =\< 12 months prior to registration.
* Unstable angina or acute coronary syndrome =\<3 months prior to registration.
* History of myocardial infarction =\< 6 months prior to registration.
* Uncontrolled or symptomatic cardiac arrhythmia.
* NOTE: Patients with pacemakers are eligible if they have no history of fainting or clinically relevant arrhythmias while using the pacemaker
* Prolongation of the QT interval corrected for heart rate (Fridericia's correction formula \[QTcF\]) \> 470 msec on at least 2/3 consecutive electrocardiograms (ECGs), and mean QTcF \> 470 msec on all 3 ECGs, during screening.
* NOTE: QTcF is calculated using Fridericia's Formula (QTcF).
* NOTE: Correction for a widened QRS complex such as pacing, underlying bundle branch block (BBB), etc. is allowed e.g., "Adjusted QTcF" = measured QTcF - (measured QRS - 90 ms).
* NOTE: Correction of suspected drug-induced QTcF prolongation can be attempted at the investigator's discretion and only if clinically safe to do so with either discontinuation of the offending drug or switch to another drug not known to be associated with QTcF prolongation.
* History of cerebral vascular accident =\< 6 months prior to registration.
* Ongoing inflammatory bowel disease (such as ulcerative colitis) requiring active treatment.
* Oxygen dependent baseline lung disease (such as interstitial lung disease or chronic obstructive pulmonary disease \[COPD\]).
* Psychiatric illness/social situations that would limit compliance with study requirements.
* Major surgery =\< 4 weeks prior to registration.
* Other active primary malignancy (other than localized non-melanotic skin cancer or carcinoma in situ of the cervix) requiring treatment or limiting expected survival to =\< 2 years.
* NOTE: If there is a history of prior malignancy, the patient must not require ongoing therapy such as radiation, chemotherapy, or immunotherapy for their cancer. Patients on hormonal therapy for adequately treated nonmetastatic breast or prostate cancer are permitted if they meet other eligibility criteria.
* Have a known hypersensitivity to any of the excipients of pirtobrutinib.
