Inclusion Criteria:

          -  Signed, informed consent

          -  Ability and willingness to comply with the requirements of the study protocol

          -  Age ≥18 years

          -  Diagnosis of the following histories according to the WHO criteria

               1. CLL or SLL

               2. MCL with TP53 mutation irrespective of variant allele frequency

          -  For patients with SLL, peripheral blood flow cytometry must be positive with CLL-like
             cells accounting for at least 1% of circulating WBC.

          -  No prior systemic therapy for disease under study except:

               1. prior local radiation for symptomatic disease is permitted

               2. Short course systemic corticosteroids is permissible for disease control,
                  improvement of performance status or non-cancer indication (must be < 7 days and
                  < 100 mg/day prednisone equivalent). Steroids must be discontinued prior to study
                  treatment. Inhaled steroids for asthma, topical steroids, and replacement/Stress
                  corticosteroids are permitted. Low-dose steroids for ITP are also permitted up to
                  the equivalent prednisone 20mg/daily at time of eligibility review.

          -  ECOG performance status of 0 to 2

          -  Adequate hematologic parameters unless due to disease under study:

               1. Absolute neutrophil count (ANC) ≥1.0 x 109/L unless neutropenia is clearly due to
                  disease under study (per investigator discretion)

               2. Platelet count ≥ 75,000/mm3 - OR - Platelet count ≥ 20,000/mm3 if
                  thrombocytopenia is clearly due to disease under study (per investigator
                  discretion)

               3. Hemoglobin ≥9.0 g/dL unless anemia is clearly due to marrow involvement due to
                  disease under study (per investigator discretion)

          -  Adequate renal and hepatic function, per laboratory reference range at Screening as
             follows:

               1. AST/SGOT, ALT/SGPT ≤2.0 x ULN

               2. Total bilirubin ≤ 2.0 x ULN unless considered secondary to Gilbert"s syndrome, in
                  which case ≤3 x ULN

               3. Creatinine clearance of eGFR>50 mL/min according to the Cockcroft-Gault Equation

          -  QT-interval corrected according to Fridericia"s formula (QTcF) ≤450 milliseconds (ms).
             Patients with documented left bundle branch block or right bundle branch block may
             have QTcF calculated with the correction listed in Appendix I.

          -  For females of childbearing potential, a negative serum pregnancy test within 7 days
             of study treatment

          -  For female patients of childbearing potential, agreement to use highly effective
             form(s) of contraception (i.e., one that results in a low failure rate [<1% per year]
             when used consistently and correctly) or remain abstinent (refrain from heterosexual
             intercourse) during the treatment period and to continue its use for 90 days after the
             last dose of zanubrutinib AND 30 days after the last dose of venetoclax AND for 18
             months after the last dose of obinutuzumab (whichever date is later)

        A woman is considered to be of childbearing potential if she is postmenarcheal, has not
        reached a postmenopausal state (>/= 12 continuous months of amenorrhea with no identified
        cause other than menopause), and it not permanently infertile due to surgery (i.e., removal
        of ovaries, fallopian tubes, and/or uterus) or another cause as determined by the
        investigator (e.g., Mullerian agenesis). The definition of childbearing potential may be
        adapted for alignment with local guidelines or regulations.

        Examples of contraceptive methods with a failure rate of <1% per year include bilateral
        tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation,
        hormone-releasing intrauterine devices, and copper intrauterine devices. Hormonal
        contraceptive methods must be supplemented by a barrier method.

        a. The reliability of sexual abstinence should be evaluated in relation to the duration of
        the clinical trial and the preferred and usual lifestyle of the patient. Periodic
        abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and
        withdrawal are not acceptable methods of contraception.

          -  For men with a female partner of childbearing potential or a pregnant female partnet:
             agreement to remain abstinent (refrain from heterosexual intercourse) or use a condom
             during the treatment period and to continue its use for 90 days after the last dose of
             zanubrutinib, or venetoclax AND for 18 months after the last dose of obinutuzumab
             (whichever date is later)

        The reliability of sexual abstinence should be evaluated in relation duration of the
        clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence
        (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not
        acceptable methods of contraception

          -  Willingness to not donate sperm or oocytes during the entire study treatment period
             and after treatment discontinuation for 90 days after the last dose of zanubrutinib
             AND 30 days after the last dose of venetoclax AND for 18 months after the last dose of
             obinutuzumab (whichever date is later)

        Additional Eligibility Criteria for CLL Cohort:

          1. Diagnosis of untreated CLL or SLL according to WHO criteria

          2. For patients with SLL, peripheral blood flow cytometry must be positive with CLL-like
             cells accounting for at least 1% of circulating WBC

          3. No prior systemic therapy for CLL: prior single site of local radiation for
             symptomatic disease is permitted

          4. Subject requires treatment according to IWCLL guidelines (See Appendix A)

        Additional Eligibility Criteria for MCL cohort:

          1. Diagnosis of untreated stage II-IV mantle cell lymphoma

             a. Prior radiotherapy for localized disease is permitted

          2. Presence of TP53 mutation irrespective of variant allele frequency

        Exclusion Criteria:

        Other malignancies:

          -  Known active histological transformation from CLL to an aggressive lymphoma (i.e.,
             Richter"s transformation)

          -  Active malignancy or systemic therapy for another malignancy within 3 years;
             local/regional therapy with curative intent such as surgical resection or localized
             radiation within 3 years of treatment is permitted

          -  Other diagnosis of active cancer

        Co-morbidities:

          -  Any uncontrolled illness that in the opinion of the investigator would preclude
             administration of study therapy (e.g. significant active infections, hypertension,
             angina, arrhythmias, pulmonary disease, or autoimmune dysfunction)

          -  Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection
             (excluding fungal infections of nail beds) at study enrollment, or any major episode
             of infection requiring treatment with IV antibiotics or hospitalization (relating to
             the completion of the course of antibiotics) within 4 weeks prior to Cycle 1, Day 1

          -  Known bleeding diathesis

          -  Prior major surgical procedure within 4 weeks of study, or anticipation of need for a
             major surgical procedure during the course of the study

          -  Known CNS hemorrhage or stroke within 6 months of the study

          -  History of progressive multifocal leukoencephalopathy (PML)

          -  History of HIV infection or active hepatitis B (chronic or acute) or hepatitis C
             infection

               1. Patients with occult or prior HBV infection (defined as positive total hepatitis
                  B core antibody [HBcAb] and negative HBsAg) may be included if HBV DNA is
                  undetectable. These patients must be willing to take appropriate anti-viral
                  prophylaxis as indicated and undergo monthly DNA testing.

               2. Patients positive for hepatitis C virus (HCV) antibody are eligible only if
                  polymerase chain reaction (PCR) is negative for HCV RNA

          -  Congestive heart failure, New York Heart Association classification III/IV

          -  Clinically significant history of liver disease, including viral or other hepatitis,
             current alcohol abuse, or cirrhosis

          -  Receipt of live-virus vaccines within 28 days prior to the initiation of study
             treatment or need for live-virus vaccines at any time during study treatment

          -  Known condition or other clinical situation that would affect oral absorption

          -  Psychiatric illness/social situations that would interfere with study compliance

          -  Inability to swallow a large number of tablets

        Concomitant medications and drug interactions:

          -  Administration within 7 days prior to the first dose of study drug or concurrent
             therapy with strong inhibitors or inducers of CYP3A, CYP2C8, CYP2C9 and CYP2C19. The
             same applied for moderate inhibitors or inducers of CY_3A

          -  Requires aspirin and P2Y inhibitors (clopidogrel, ticagrelor)

          -  Live-virus vaccines given within 28 days prior to the initiation of study treatment

          -  Immunotherapy

          -  Hormone therapy (other than contraceptives, hormone replacement therapy, or megestrol
             acetate)

          -  Any therapies intended for the treatment of lymphoma/leukemia whether FDA approved or
             experimental (outside of this study)

          -  Radiation therapy intended to treat MCL or CLL/SLL

          -  Warfarin or warfarin derivatives

          -  Consumption of one or more of the following within 3 days prior to the first dose of
             study drug:

        Grapefruit or grapefruit products Seville oranges, including marmalade containing Seville
        oranges Star Fruit (carambola)

        Prior therapy:

          -  Prior anti-CD20 monoclonal antibody therapy for non-malignant indication

          -  Obinutuzumab is contraindicated in patients with a known hypersensitivity
             (IgE-mediated) reaction to obinutuzumab or to any of its excipients

          -  Prior systemic therapy for CLL; prior single site of local radiation for symptomatic
             disease is permitted

        Other:

          -  Females who are currently pregnant or breastfeeding

          -  Participation in a separate investigational therapeutic study unless authorized by the
             investigator