Inclusion Criteria:

          -  Depending upon study part: a history or status of a histologically-confirmed
             hematological malignancy that is expected to express CD19 and CD20; relapse after or
             failure to respond to at least two prior treatment regimens; and no available
             treatment options that are expected to prolong survival

          -  Must have at least one measureable target lesion (>/= 1.5 cm) in its largest dimension
             by computed tomography scan

          -  Able and willing to provide a fresh biopsy from a safely accessible site, per
             Investigator's determination, providing the participant has more than one measurable
             target lesion

          -  Eastern Cooperative Oncology Group performance status of 0 or 1

          -  Life expectancy of >/= 12 weeks

          -  Adverse events from prior anti-cancer therapy must have resolved to Grade </= 1

          -  Adequate liver, haematological, and renal function

          -  Negative test results for acute or chronic hepatitis B virus infection

          -  Negative test results for hepatitis C virus and HIV

          -  The contraception and abstinence requirements are intended to prevent exposure of an
             embryo to the study treatment. The reliability of sexual abstinence for male and/or
             female enrollment eligibility needs to be evaluated in relation to the duration of the
             clinical study and the preferred and usual lifestyle of the participant. Periodic
             abstinence (e.g., calendar, ovulation, symptothermal, or post-ovulation methods) and
             withdrawal are not acceptable methods of preventing drug exposure

          -  Female participants: A female participant is eligible to participate if she is not
             pregnant and not breastfeeding, and if at least one of the following applies: women of
             non-childbearing potential (WONCBP); women of child bearing potential (WOCBP) who
             agree to remain abstinent or use two highly effective contraceptive methods with a
             failure rate of <1% per year during the treatment period and for at least 18 months
             after obinutuzumab or 3.5 months after the last dose of RO7227166, 2 months after last
             dose of glofitamab, or 3 months after the last dose of tocilizumab, whichever is
             longer. Examples of contraceptive methods with a failure rate of < 1% per year include
             bilateral tubal occlusion/ ligation, male sexual partner who is sterilized,
             established proper use of hormonal contraceptives that inhibit ovulation,
             hormone-releasing intrauterine devices and copper intrauterine devices. Hormonal
             contraceptive methods must be supplemented by a barrier method; have a negative
             pregnancy test (blood) within the 7 days prior to the first study treatment
             administration

          -  Male participants: During the treatment period and for at least 3 months after
             obinutuzumab, or 2 months after the last dose of RO7227166, glofitamab, or tocilizumab
             whichever is longer, agreement to: Remain abstinent or use contraceptive measures such
             as a condom plus an additional contraceptive method that together result in a failure
             rate of < 1% per year, with a partner who is a women of childbearing potential. With
             pregnant female partner, remain abstinent or use contraceptive measures such as a
             condom to avoid exposing the embryo; refrain from donating sperm during this same
             period

        Exclusion Criteria:

          -  Circulating lymphoma cells, defined by out of range (high) absolute lymphocyte count
             or the presence of abnormal cells in the peripheral blood differential signifying
             circulating lymphoma cells

          -  Participants with acute bacterial, viral, or fungal infection at baseline, confirmed
             by a positive blood culture within 72 hours prior to obinutuzumab infusion or by
             clinical judgment in the absence of a positive blood culture

          -  Participants with known active infection, or reactivation of a latent infection,
             whether bacterial, viral fungal, mycobacterial, or other pathogens (excluding fungal
             infections of nail beds) or any major episode of infection requiring hospitalization
             or treatment with IV antibiotics

          -  Pregnant or breast-feeding or intending to become pregnant during the study

          -  Prior treatment with systemic immunotherapeutic agents, including, but not limited to,
             radio-immunoconjugates, antibody-drug conjugates, immune/cytokines or monoclonal
             antibodies within 4 weeks or five half-lives of the drug, whichever is longer, before
             obinutuzumab infusion on D-7

          -  History of treatment-emergent immune-related AEs associated with prior
             immunotherapeutic agents and auto-immune disease

          -  Treatment with standard radiotherapy, any chemotherapeutic agent, or treatment with
             any other investigational or approved anti-cancer agent within 4 weeks or 5 half-lives
             of the drug, whichever is longer, prior to obinutuzumab infusion

          -  Prior solid organ transplantation

          -  Prior allogeneic stem cell transplant (SCT) and prior chimeric antigen receptor
             -T-cell therapy

          -  Autologous SCT within 100 days prior to obinutuzumab infusion

          -  History of severe allergic or anaphylactic reactions to monoclonal antibody therapy
             and confirmed progressive multifocal leukoencephalopathy

          -  Current or past history of central nervous system (CNS) lymphoma and CNS disease

          -  Evidence of significant, uncontrolled concomitant diseases that could affect
             compliance with the protocol or interpretation of results, including diabetes
             mellitus, history of relevant pulmonary disorders and known autoimmune diseases

          -  Major surgery or significant traumatic injury < 28 days prior to the Gpt infusion or
             anticipation of the need for major surgery during study treatment

          -  Participants with another invasive malignancy in the last 2 years

          -  Significant cardiovascular disease

          -  Administration of a live, attenuated vaccine within 4 weeks before Gpt infusion or
             anticipation that such a live attenuated vaccine will be required during the study

          -  Received systemic immunosuppressive medications (including but not limited to
             cyclohosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis
             factor agents) with the exception of corticosteroid treatment <=25 mg/day of
             prednisone or equivalent, however there must be documentation that the participant was
             on a stable dose of at least a 2-week duration prior to Gpt infusion. Inhaled and
             topical steriods are permitted