A Study of Atezolizumab in Combination With an Immunotherapy Agent Investigated With or Without Anti-Cd20 Therapy in Patients With Relapsed or Refractory Non-Hodgkin Lymphoma

Inclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) Performance Status of 0, 1, or 2 * Life expectancy ≥ 12 weeks * At least two bi-dimensionally measurable nodal lesions ≥ 1.5 centimeters (cm) in its longest diameter by imaging * Adequate hematologic and end-organ function * For women of childbearing potential: agreement to remain abstinent * For men: agreement to remain abstinent or use contraceptive measures and agreement to refrain from donating sperm * Consent to collection of a pre-treatment tumor sample, on-treatment biopsy, and, if applicable, a tumor tissue sample at the time of progressive disease (PD) Inclusion Criteria Specific to Obinutuzumab-Containing Cohorts \- Patients receiving therapeutic anticoagulation should be switched to low molecular weight heparin (LMWH) before the first cycle of obinutuzumab Exclusion Criteria: * Any approved systemic anti-cancer therapy (including chemotherapy) or hormonal therapy within 3 weeks prior to initiation of study treatment * Treatment with any other investigational agent or participation in another clinical study with therapeutic intent within 28 days prior to enrollment * Known central nervous system (CNS) lymphoma, leptomeningeal lymphoma * Grade 3b FL, small lymphocytic lymphoma (SLL), Waldenström macroglobulinemia (WM), or other lymphoma subtypes except as stated in the inclusion criteria * Uncontrolled tumor-related pain * Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures * Uncontrolled hypercalcemia * History of other malignancy within 5 years prior to screening with the exception of malignancies with a negligible risk of metastasis or death, such as adequately treated carcinoma in situ of the cervix, non-melanoma skin carcinoma, localized prostate cancer, ductal carcinoma in situ, or Stage I uterine cancer * Known hypersensitivity to any of the study drugs * History of sensitivity to mannitol * Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection * Pregnant and lactating women * History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins * Known hypersensitivity to biopharmaceuticals produced in Chinese hamster ovary cells or any component of the atezolizumab formulation, emactuzumab formulation, or obinutuzumab formulation * History of autoimmune disease, including, but not limited to, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis (RA), inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener granulomatosis, Sjögren syndrome, Guillain-Barre syndrome, multiple sclerosis, vasculitis, or glomerulonephritis * Patients with prior allogeneic bone marrow transplantation or prior solid organ transplantation * History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, idiopathic pneumonitis, or evidence of active pneumonitis per chest computed tomography (CT) scan at screening * Serum albumin \< 2.5 g/dL * Positive test for HIV (human immunodeficiency virus) * All patients will have a tuberculin (purified protein derivative \[PPD\]) skin test or interferon-gamma release assay (IGRA) done locally prior to the inclusion into the study. Patients with active tuberculosis (TB) will be excluded from the study. * History of chronic hepatitis B virus (HBV) infection or positive test results for active or chronic HBV infection defined by hepatitis B surface antigen (HBsAg) * Patients with active or chronic hepatitis C virus (HCV) * Active TB * Signs or symptoms of infection within 2 weeks prior to Cycle 1, Day 1 * Significant cardiovascular disease, such as cardiac disease, myocardial infarction within the previous 3 months, unstable arrhythmias, or unstable angina * Major surgical procedure other than for diagnosis within 28 days prior to Cycle 1, Day 1 or anticipation of a major surgical procedure during the course of the study * Administration of a live, attenuated vaccine within 4 weeks before Cycle 1, Day 1 or anticipation that such a live attenuated vaccine will be required during the study * Prior treatment with CD137 agonists or immune checkpoint blockade therapies * Treatment with systemic immunosuppressive medications (including, but not limited to, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor (TNF)) within 2 weeks prior to Cycle 1, Day 1 * The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) is allowed Exclusion Criteria Specific to Obinutuzumab-Containing Cohorts: Hypersensitivity to obinutuzumab * Prior treatment with obinutuzumab * Fludarabine or Campath within 12 months prior to study entry * History of severe allergic or anaphylactic reactions to monoclonal antibody therapy (e.g., patients in whom dosing with obinutuzumab would be contraindicated for safety reasons) * Received therapeutic oral or IV antibiotics within 4 weeks prior to Cycle 1, Day 1 (except for tumor fever) * Patients with history of confirmed progressive multifocal leukoencephalopathy * Regular treatment with corticosteroids within the 4 weeks prior to the start of Cycle 1, unless administered for indications other than NHL at a dose equivalent to \< 30 mg/day prednisone/prednisolone