This open-label, multicenter, global study is designed to assess the safety, tolerability, preliminary efficacy, and pharmacokinetics of intravenous atezolizumab (MPDL3280A) and obinutuzumab in participants with refractory or relapsed follicular lymphoma (FL) or atezolizumab and obinutuzumab or tazemetostat administered in participants with refractory or relapsed diffuse large B-cell lymphoma (DLBCL). The anticipated duration of this study is approximately 4.5 years.

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