A Study Evaluating Safety and Efficacy of Obinutuzumab, Polatuzumab Vedotin (Pola), and Atezolizumab (Atezo) in Participants With Relapsed or Refractory Follicular Lymphoma (FL) and Rituximab, Atezo, and Pola in Participants With Relapsed or Refractory Diffuse Large B-Cell Lymphoma (DLBCL)

This study will evaluate the safety, efficacy, pharmacokinetics, and immunogenicity of obinutuzumab + Atezo + Pola in participants with relapsed or refractory (RR) FL and rituximab + Atezo + Pola in participants with RR DLBCL. The study will include an initial dose-escalation phase designed to determine the recommended Phase 2 dose (RP2D) for Pola in this treatment combination, followed by an expansion phase in which Pola will be given at the RP2D. All participants will receive induction treatment with obinutuzumab + Atezo + Pola for 6 cycles. RR FL participants achieving a complete response (CR), partial response (PR), or stable disease (SD) at the end of induction (EOI) will receive maintenance treatment with obinutuzumab.


Eligibility Criteria:
Inclusion Criteria:

* Eastern Cooperative Oncology Group (ECOG) Performance Status of 0, 1, or 2
* For obinutuzumab + Atezo + Pola treatment group: relapsed or refractory FL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-Cluster of Differentiation (CD)20 monoclonal antibody and for which no other more appropriate treatment option exists as determined by the investigator
* For rituximab + Atezo + Pola treatment group: relapsed or refractory DLBCL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-CD20 monoclonal antibody, in participants who are not eligible for second line combination (immuno-) chemotherapy and autologous stem-cell transplantation or who have failed second line combination (immuno-) chemotherapy or experienced disease progression following autologous stem-cell transplantation
* Histologically documented CD20-positive lymphoma and fluorodeoxyglucose (FDG)-avid lymphoma (that is PET-positive lymphoma) with at least one bi-dimensionally measurable lesion
* 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 or to use contraceptive methods that result in a failure rate of less than (\<) 1% per year during the treatment period for greater than or equal to (\>=) 5 months after last dose of Atezo, \>= 12 months after last dose of rituximab, \>= 12 months after last dose of Pola, and \>= 18 months after last dose of obinutuzumab
* For men: agreement to remain abstinent or to use contraceptive measures that result in a failure rate of \<1% per year during the treatment period and for at least 3 months after last dose of obinutuzumab, rituximab, and Atezo and for 5 months after last dose of Pola, and agreement to refrain from donating sperm during this same period

Exclusion Criteria:

* Grade 3b follicular lymphoma
* History of transformation of indolent disease to DLBCL
* Known CD20-negative status at relapse or progression; CNS lymphoma or leptomeningeal infiltration
* Prior allogeneic stem cell transplantation (SCT), completion of autologous SCT within 100 days prior to Day 1 of Cycle 1 (D1C1)
* Prior anti-cancer therapy including: Fludarabine or alemtuzumab within 12 months prior to D1C1; radioimmunoconjugate within 12 weeks prior to D1C1; monoclonal antibody or antibody drug conjugate (ADC) within 5 half-lives or 4 weeks prior to D1C1 ; radiotherapy, chemotherapy, hormonal therapy, or targeted small-molecule therapy within 2 weeks prior to D1C1; anti-programmed death-1 (anti-PD-1), anti-programmed death-ligand 1 (anti-PD-L1), anti-cytotoxic T-lymphocyte-associated protein 4 (CTLA4), anti-CD137/41-BB agonist, or anti-CD40 agonist antibodies
* 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 D1C1
* History of solid organ transplantation and of severe allergic or anaphylactic reaction to humanized, chimeric, or murine monoclonal antibodies
* Active infection; positive for hepatitis B surface agent (HbsAg), total hepatitis B core antibody (HBcAb), or hepatitis C virus (HCV) antibody at screening; known history of HIV positive status, progressive multifocal leukoencephalopathy (PML), autoimmune disease
* Vaccination with a live virus vaccine or live attenuated vaccine within 28 days prior to D1C1
* Pre-existing Grade greater than (\>) 1 neuropathy
* Major surgical procedure other than for diagnosis within 28 days prior to D1C1
* Inadequate hematologic function, renal function, and liver function
* Pregnant or lactating women
* Life expectancy \< 3 months