Amazon Lambda is like Microsoft Windows was in its early stages. It's a fast-growing, closed/proprietary system for running apps. I wouldn't be surprised if it achieves a near-monopoly for a while... But I think that eventually more flexible open source solutions will take over. Open platforms like Docker and Kubernetes will likely replace Lambda just as Linux replaced Windows on the server-side.
I am not sure if Docker/Kubernetes are comparable with Lambda. But currently there are some attempts to develop an open source alternative to Lambda and other proprietary FaaS (Function as a Service) platforms like OpenWhisk for Cloud Foundry: http://openwhisk.org/