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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

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