This Phase Ib/II, open-label, multicenter, non-randomized study will evaluate the safety, efficacy, and pharmacokinetics of induction treatment consisting of atezolizumab in combination with either obinutuzumab + bendamustine (Atezo-G-benda) or obinutuzumab + CHOP (Atezo-G-CHOP) in participants with FL and atezolizumab + rituximab + chemotherapy (Atezo-R-CHOP) in participants with DLBCL, followed by post-induction treatment consisting of either atezolizumab plus obinutuzumab (Atezo-G) in participants with FL who achieve a complete response (CR) or partial response (PR) at end of induction (EOI) or atezolizumab alone in participants with DLBCL who achieve a CR at EOI.