Inclusion Criteria:

          -  Patients will have a diagnosis of CLL or small lymphocytic lymphoma (SLL), refractory
             to or relapsed after at least one prior standard therapy or untreated with deletion
             (del)(17p) by fluorescence in-situ hybridization (FISH) (high-risk cytogenetics) and
             have an indication for treatment by IWCLL 2008 criteria (Cohort 1) OR have been on
             ibrutinib for at least 9 months with measurable persistent disease (absolute
             lymphocyte count [ALC] > 4 K/muL, any lymph node > 1.5 cm by computed tomography [CT]
             scan, or > 30% lymphocytes on bone marrow aspirate differential) (Cohort 2), OR
             patients will have a diagnosis of RT, refractory to and/or relapsed after at least one
             prior standard therapy or untreated with del(17p) by FISH (high-risk cytogenetics)
             (Cohort 3)

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2

          -  Total bilirubin =< 1.5 x upper limit of normal (ULN); for patients with Gilbert's
             disease, total bilirubin up to =< 3 x ULN is allowed provided normal direct bilirubin

          -  Serum creatinine =< 1.5 x ULN

          -  Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =< 3 x ULN

          -  Females of childbearing potential must have a negative serum or urine beta human
             chorionic gonadotrophin (beta-hCG) pregnancy test result within 24 hours prior to the
             first dose of treatment and must agree to use an effective contraception method during
             the study and for 23 weeks following the last dose of the study drugs; females of
             non-childbearing potential are those who are postmenopausal greater than 1 year or who
             have had a bilateral tubal ligation or hysterectomy; males who have partners of
             childbearing potential must agree to use an effective contraceptive method during the
             study and for 31 weeks following the last dose of study drugs

          -  Patients or their legally authorized representative must provide written informed
             consent

        Exclusion Criteria:

          -  History of another primary invasive malignancy that has not been definitively treated
             or in remission for at least 2 years; patients with non-melanoma skin cancers or with
             carcinomas in situ are eligible regardless of the time from diagnosis (including
             concomitant diagnoses); if patients have another malignancy that was treated within
             the last 2 years, such patients may be enrolled if the likelihood of requiring
             systemic therapy for this other malignancy within 2 years is less than 10%, as
             determined by an expert in that particular malignancy at MD Anderson Cancer Center and
             after consultation with the principal investigator

          -  Any major surgery, radiotherapy, cytotoxic chemotherapy, biologic therapy,
             immunotherapy, immunomodulatory drugs, experimental therapy within 4 weeks prior to
             the first dose of the study drugs; Note: prior therapy with anti cluster of
             differentiation (CD)20 monoclonal antibody, anti CD52 monoclonal antibody, and
             lenalidomide are allowed; for oral targeted therapies (such as idelalisib,
             venetoclax), a washout of 3 days is allowed

          -  Significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias,
             congestive heart failure, or myocardial infarction within 2 months of screening, or
             any class 3 or 4 cardiac disease as defined by the New York Heart Association
             functional classification

          -  History of stroke or cerebral hemorrhage within 2 month

          -  Patients who have uncontrolled hypertension (defined as sustained systolic blood
             pressure >= 160 mmHg or diastolic >= 100 mmHg)

          -  Known evidence of active cerebral/meningeal CLL; patients may have history of central
             nervous system (CNS) leukemic involvement if definitively treated with prior therapy
             and no evidence of active disease at the time of registration

          -  Active, uncontrolled autoimmune hemolytic anemia or immune thrombocytopenia requiring
             steroid therapy

          -  Patients with autoimmune diseases are excluded: patients with a history of
             inflammatory bowel disease (including Crohn's disease and ulcerative colitis) are
             excluded from this study as are patients with a history of autoimmune disease (e.g.,
             rheumatoid arthritis, systemic progressive sclerosis, systemic lupus erythematosus,
             Wegener's granulomatosis)

          -  Patients with previous allogeneic stem cell transplant (SCT) within 6 months or with
             active acute or chronic graft-versus host disease are excluded; patients must be off
             immunosuppression for graft-versus host disease (GVHD) for at least 30 days before
             cycle 1 day 1

          -  Patients with organ allografts (such as renal transplant) are excluded

          -  History of interstitial lung disease or pneumonitis

          -  Patients who are on high dose steroid (> 10 mg daily of prednisone or equivalent) or
             immune suppression medications; Note: patients on high-dose steroids (doses > 10mg/day
             of prednisone or equivalent) or immune suppression medications are eligible provided
             these drugs are discontinued at least 3 days prior to starting on the study drugs

          -  Patients with uncontrolled active infection (viral, bacterial, and fungal) are not
             eligible

          -  Current or chronic hepatitis B or C infection, or known seropositivity for human
             immunodeficiency virus (HIV)

          -  Patient is pregnant or breast-feeding

          -  Concurrent use of investigational therapeutic agent

          -  Malabsorption syndrome or other condition that precludes enteral route of
             administration

          -  Concomitant use of warfarin or other vitamin K antagonists

          -  Requires treatment with a strong cytochrome P450 (CYP) family 3, subfamily A (3A)
             inhibitor

          -  Other severe acute or chronic medical or psychiatric condition or laboratory
             abnormality that in the opinion of the investigator may increase the risk associated
             with study participation or investigational product administration or may interfere
             with the interpretation of study results and/or would make the patient inappropriate
             for enrollment into this study