A Safety and Pharmacology Study of Atezolizumab (MPDL3280A) Administered With Obinutuzumab or Tazemetostat in Participants With Relapsed/Refractory Follicular Lymphoma and Diffuse Large B-cell Lymphoma

Inclusion Criteria:

* Histologically documented, CD20-positive, relapsed or refractory (defined as having relapsed within 6 months to the previous treatment) FL or DLBCL (including primary mediastinal large B-cell lymphoma \[PMLBCL\])
* Bone marrow biopsy at screening (unless it was performed within 3 months prior to screening)
* Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2
* Life expectancy greater than or equal to (\>=) 12 weeks
* Has a QT interval corrected by Fridericia's formula (QTcF) less than or equal to (\<=) 480 milliseconds (msec)
* At least one bi-dimensionally measurable nodal lesion \>1.5 cm in its longest diameter by computed tomography (CT) scan or MRI, as defined by the Lugano Classification
* Adequate hematologic and end-organ function
* Archival tumor tissue
* For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods that result in a failure rate of \< 1% per year during the treatment period and for at least 90 days after the last dose of atezolizumab or 18 months after the last dose of obinutuzumab, whichever is longer
* For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures and agreement to refrain from donating sperm

Exclusion Criteria:

* Known central nervous system lymphoma, leptomeningeal lymphoma, or histologic evidence of transformation from an indolent lymphoma to a high-grade or DLBCL
* Grade 3b FL, small lymphocytic lymphoma (SLL), or Waldenström's macroglobulinemia (WM) or other lymphoma subtypes except as stated in the inclusion criteria
* Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures (once monthly or more frequently); participants with indwelling catheters are eligible
* Uncontrolled hypercalcemia or symptomatic hypercalcemia requiring continued use of bisphosphonate therapy or denosumab
* History of severe allergic or anaphylactic reactions to monoclonal antibody therapy
* Has had prior exposure to tazemetostat or other inhibitor(s) of enhancer of zeste homolog 2 (EZH2)
* Regular treatment with corticosteroids within the 2 or 4 weeks prior to the start of Cycle 1, unless administered for indications other than non-Hodgkin's lymphoma at a dose equivalent to \< 30 mg/day prednisone/prednisolone
* Pregnant and lactating women
* History of autoimmune disease
* Participants with history of confirmed progressive multifocal leukoencephalopathy (PML)
* Participants with prior allogeneic bone marrow transplantation or prior solid organ transplantation
* History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, idiopathic pneumonitis, or evidence of active pneumonitis per chest CT scan at screening. History of radiation pneumonitis in the radiation field (fibrosis) is allowed
* Positive test for Human Immunodeficiency Virus (HIV)
* History of chronic hepatitis B infection or positive test results for active or chronic hepatitis B or hepatitis C
* Significant cardiovascular disease, such as cardiac disease (New York Heart Association Class II or greater), myocardial infarction within the previous 3 months, unstable arrhythmias, or unstable angina
* Hypersensitivity or prior treatment with obinutuzumab
* Fludarabine or Campath within 12 months prior to study entry
* Prior treatment with CD137 agonists or immune checkpoint blockade therapies, including anti-CTLA4, anti-PD-1, and anti-PD-L1 therapeutic antibodies
* Treatment with systemic immunostimulatory agents (including but not limited to interferon, interleukin-2) within 6 weeks or 5 half-lives of the drug, whichever is shorter, prior to Cycle 1, Day 1
* Treatment with systemic immunosuppressive medications, including but not limited to prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor (anti-TNF) agents within 2 weeks prior to Cycle 1, Day 1; inhaled corticosteroids and mineralocorticoids are allowed
* Participants with active tuberculosis (TB) will be excluded from the clinical trial