A Study of Atezolizumab (MPDL3280A) in Combination With Epacadostat (INCB024360) in Subjects With Previously Treated Stage IIIB or Stage IV Non-Small Cell Lung Cancer and Previously Treated Stage IV Urothelial Carcinoma (ECHO-110)

Inclusion Criteria: * Male or female subjects, age 18 years or older * Histologically or cytologically confirmed NSCLC * Stage IIIB or Stage IV NSCLC who are not candidates for multimodality treatment and have received at least 1 line of standard platinum-based therapy: * Prior systemic regimens must include at least 2 cycles of a platinum-based therapy and may include platinum therapy used as a radiosensitizer. Maintenance chemotherapy is allowed. * Tumors with driver mutations (epidermal growth factor receptor mutation positive or anaplastic lymphoma kinase fusion oncogene positive) should have had disease progression or been intolerant to the standard tyrosine-kinase inhibitor (TKI), and should include a second line TKI where such therapy is available and indicated. * Subjects initially treated with a platinum regimen for Stage IIIB disease who later develop metastatic disease and are re-treated with a platinum regimen are allowed. * Histologically or cytologically confirmed urothelial carcinoma. * Stage IV locally advanced or metastatic urothelial carcinoma with disease progression during or following platinum-containing chemotherapy or had disease progression within 12 months of neoadjuvant or adjuvant treatment with platinum-containing chemotherapy. * Eastern Cooperative Oncology Group (ECOG) performance status 0 to 1. * Presence of measurable disease per RECIST v1.1 * Availability of an adequate archival tumor specimen or willingness to undergo a pretreatment tumor biopsy. * Subjects enrolled in Expansion Cohort 3 must be willing to have 2 on-treatment tumor biopsies. * For males and females of child-bearing potential, willingness to use adequate birth control through 90 days after the last dose of epacadostat or atezolizumab. Exclusion Criteria: * Laboratory and medical history parameters not within protocol-defined range. * Current treatment with an investigational study drug or immunological-based agent for any reason, or receipt of anticancer medication within 21 days or 5 half-lives (whichever is longer) before first dose. * Prior treatment with immune checkpoint inhibitors (eg, anti-CTLA-4, anti-PD-1, anti-PD-L1, and any other antibody or drug specifically targeting T-cell co-stimulation) or an IDO inhibitor. * Prior monoclonal antibody within 4 weeks before study Day 1, or has not recovered from adverse events due to agents administered more than 4 weeks earlier. * Has an active or inactive autoimmune process. * Has a history of pneumonitis or idiopathic pulmonary fibrosis, or evidence of interstitial lung disease. * Prior radiotherapy within 2 weeks of therapy; Must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. * Untreated central nervous system (CNS) metastases or CNS metastases that have progressed after completion of radiotherapy. * Use of systemic corticosteroids ≤ 2 weeks before Cycle 1 Day 1. * Currently pregnant or breastfeeding.