A Study of Atezolizumab in Combination With Either Obinutuzumab Plus Bendamustine or Obinutuzumab Plus (+) Cyclophosphamide, Doxorubicin, Vincristine, and Prednisone (CHOP) in Participants With Follicular Lymphoma (FL) or Rituximab + CHOP in Participants With Diffuse Large B-Cell Lymphoma (DLBCL)

Inclusion Criteria:

* Eastern Cooperative Oncology Group (ECOG) Performance Status of 0, 1, or 2
* For participants enrolled in the safety run-in phase: lymphoma classified as either relapsed or refractory FL after treatment with at least one prior chemoimmunotherapy regimen or previously untreated Grade 1, 2, or 3a FL that requires treatment
* For participants enrolled in the expansion phase: lymphoma classified as either previously untreated Grade 1, 2, or 3a FL that requires treatment or previously untreated advanced DLBCL
* Histologically documented cluster of differentiation 20 (CD20) positive lymphoma
* Fluorodeoxyglucose-avid lymphoma
* At least one bi-dimensionally measurable lesion (greater than \[\>\] 1.5 centimeters in its largest dimension by CT scan or magnetic resonance imaging)
* Availability of a representative tumor specimen and the corresponding pathology report for retrospective central confirmation of the diagnosis of FL or DLBCL
* For women who are not postmenopausal or surgically sterile: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods that result in a failure rate of less than \[\<\] 1 percent \[%\] per year during the treatment period and for at least 18 months after the last dose of study treatment for participants in the Atezo-G-benda and Atezo-G-CHOP treatment groups or for at least 12 months after the last dose of study treatment for participants in the Atezo-R-CHOP treatment group
* For men: agreement to remain abstinent or use contraceptive measures and agreement to refrain from donating sperm

Exclusion Criteria:

* Histological evidence of transformation of FL into high-grade B-cell non-Hodgkin's lymphoma (NHL)
* Central nervous system lymphoma or leptomeningeal infiltration
* For participants with DLBCL: preplanned consolidative radiotherapy
* Treatment with systemic immunosuppressive medications, including, but not limited to, prednisone, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor agents within 2 weeks prior to Day 1 of Cycle 1
* For participants with relapsed or refractory FL: prior allogeneic or autologous stem cell transplantation, anthracycline therapy, treatment with fludarabine or alemtuzumab within 12 months prior to Day 1 of Cycle 1, treatment with a monoclonal antibody, radioimmunoconjugate, or antibody-drug conjugate within 4 weeks prior to Day 1 of Cycle 1, radiotherapy, chemotherapy, hormonal therapy, or targeted small-molecule therapy within 2 weeks prior to Day 1 of Cycle 1
* History of solid organ transplantation
* History of severe allergic or anaphylactic reaction or known sensitivity to humanized or murine monoclonal antibodies
* Known hypersensitivity to biopharmaceuticals produced in Chinese hamster ovary cells or any component of the atezolizumab, obinutuzumab, rituximab, or bendamustine formulation, including mannitol
* Positive for hepatitis B surface antigen (HBsAg), total hepatitis B core antibody (HBcAb), or hepatitis C virus (HCV) antibody at screening
* History of progressive multifocal leukoencephalopathy
* Vaccination with a live virus vaccine within 28 days prior to Day 1 of Cycle 1
* History of other malignancy, autoimmune disease, or any significant, uncontrolled concomitant disease that could affect compliance with the protocol or interpretation of results
* Major surgical procedure other than for diagnosis within 28 days prior to Day 1 of Cycle 1, or anticipation of a major surgical procedure during the course of the study
* For participants who will be receiving CHOP: left ventricular ejection fraction (LVEF) \<50% by multiple-gated acquisition (MUGA) scan or echocardiogram
* Inadequate hematologic, renal, and liver function (unless due to underlying lymphoma)