Inclusion Criteria:

- Eastern Cooperative Oncology Group (ECOG) A21 Status of 0, 1, or 2

- For participants enrolled in the dose-escalation phase: relapsed or refractory FL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-CD20 monoclonal antibody and for which no other more appropriate treatment option exists as determined by the investigator

- For participants enrolled in the expansion phase: lymphoma classified as either relapsed or refractory FL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-CD20 monoclonal antibody and for which not other more appropriate treatment option exists as determined by the investigator OR classified as Relapsed or refractory DLBCL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-CD20 monoclonal antibody, in patients who are not eligible for second line combination chemotherapy and autologous stem-cell transplantation or who have failed second line combination chemotherapy or experienced disease progression following autologous stem-cell transplantation

- Histologically documented CD20-positive lymphoma and fluorodeoxyglucose (FDG)-avid lymphoma (that is positron emission tomography [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 <1% per year during the treatment period for >= 18 months after the 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 5 months after last dose of study drug, 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; central nervous system (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 months 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 cell death protein 1 (anti PD-1), anti programmed death-ligand 1 (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 > 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 less than (<) 3 months