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