Inclusion Criteria:

          -  Depending upon study part, a history or status of: 1) a histologically-confirmed
             hematological malignancy that is expected to express cluster of differentiation
             (CD)20; 2) relapse after or failure to respond to at least one prior treatment
             regimen; and 3) no available treatment options that are expected to prolong survival
             (e.g., standard chemotherapy or autologous stem cell transplant [ASCT])

          -  Measurable disease, defined as at lease one bi-dimensionally measurable nodal lesion,
             defined as > 1.5 cm in its longest dimension, or at least one bi-dimensionally
             measureable extranodal lesion, defined as > 1.0 cm in its longest dimension

          -  Able to provide a fresh biopsy from a safely accessible site, per investigator
             determination, providing the patient has more than one measurable target lesion

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1

          -  Life expectancy of >/=12 weeks

          -  AEs from prior anti-cancer therapy must have resolved to Grade less than or equal to
             (</=) 1

          -  Adequate liver, hematological and renal function

          -  Negative serologic or polymerase chain reaction (PCR) test results for acute or
             chronic Hepatitis B virus (HBV) infection

          -  Negative test results for Hepatitis C virus (HCV) and human immunodeficiency virus
             (HIV)

          -  Negative serum pregnancy test within 7 days prior to study treatment in women of
             childbearing potential. Women who are not of childbearing potential who are considered
             to be post-menopausal (at least 12 months of non-therapy amenorrhea) or surgically
             sterile (absence of ovaries and/or uterus) are not required to have a pregnancy test

        Exclusion Criteria:

          -  Inability to comply with protocol mandated hospitalizations and restrictions

          -  Participants with chronic lymphocytic leukemia (CLL), Burkitt lymphoma and
             lymphoplasmacytic lymphoma

          -  Participants with a known or suspected history of hemophagocytic lymphohistiocytosis
             (HLH)

          -  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 or any major
             episode of infection requiring hospitalization or treatment with IV antibiotics within
             4 weeks of dosing

          -  Prior treatment with systemic immunotherapeutic agents, including, but not limited to,
             radio-immunoconjugates, antibody-drug conjugates, immune/cytokines and monoclonal
             antibodies (e.g., anti-cytotoxic T-lymphocyte-associated protein 4 [anti-CTLA4],
             anti-programmed death 1 [anti-PD1] and anti-programmed death ligand 1 [anti-PDL1])
             within 4 weeks or five half-lives of the drug, whichever is shorter, before
             obinutuzumab infusion on Cycle 1 Day -7

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

          -  Documented refractoriness to an obinutuzumab-containing regimen

          -  Treatment with standard radiotherapy, any chemotherapeutic agent, or treatment with
             any other investigational anti-cancer agent, including chimeric antigen receptor
             therapy (CAR-T) within 4 weeks prior to obinutuzumab infusion

          -  Prior solid organ transplantation

          -  Prior allogeneic SCT

          -  Autologous SCT within 100 days prior to obinutuzumab infusion

          -  Participant with history of confirmed progressive multifocal leukoencephalopathy (PML)

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

          -  Current or past history of CNS disease, such as stroke, epilepsy, CNS vasculitis, or
             neurodegenerative disease. Participants with a past history of stroke that have not
             experienced a stroke or transient ischemic attack in the past 2 years and have no
             residual neurologic deficits are allowed.

          -  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

          -  Participants with another invasive malignancy in the last 2 years (with the exception
             of basal cell carcinoma and tumors deemed by the Investigator to be of low likelihood
             for recurrence)

          -  Significant cardiovascular disease such as New York Heart Association Class III or IV
             cardiac disease, myocardial infarction within the last 6 months, unstable arrhythmias,
             or unstable angina

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

          -  Received systemic immunosuppressive medications (including but not limited to
             cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis
             factor agents) within two weeks prior to obinutuzumab infusion. Treatment with
             corticosteroid </= 25 mg/day prednisone or equivalent is allowed. Inhaled and topical
             steroids are permitted.

          -  Any other diseases, metabolic dysfunction, physical examination finding, or clinical
             laboratory finding giving reasonable suspicion of a disease or condition that would
             contraindicate the use of an investigational drug

          -  History of autoimmune disease, including but not limited to myocarditis, pneumonitis,
             myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus, erythematosus,
             rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with
             antiphospholipid syndrome, Wegener's granulomatosis, Sjögren's syndrome,
             Guillain-Barré syndrome, multiple sclerosis, vasculitis, or glomerulonephritis.
             Participants with a remote history of, or well controlled autoimmune disease, may be
             eligible to enroll after discussion with and confirmation by the Medical Monitor

          -  In Part III DLBCL dexamethasone cohort, patients with a history of hypersensitivity to
             dexamethasone or systemic corticosteroids will be excluded