We (hi, I work at Lyst too!) see Docker images as fairly similar to pre-built AMIs conceptually, just a lot more lightweight. We bake our Docker host AMIs relatively regularly and use them in the ASG that runs the Dockerized website. Building AMIs (and booting new instances from them on each deploy) takes a lot longer than building a new Docker image and launching containers from it.

I'm not entirely sure I understand what you're asking though. We've so far only Dockerized the main Python application, and not many of the supporting applications. We don't think we'd go down the route of running Postgres, ElasticSearch, Redis etc under Docker.

To give you an example of times taken, Pull Requests take about 10 minutes to test, a full master build (including uploading build artifacts) takes around 15 minutes, and a deployment to 8 Dockerized web hosts is about 5 minutes, including a smoke test on each host.

EDIT: Just realised what you're asking. If you're running many processes on each host then yes it can take a while to deploy. We deploy our Celery workers under separate Docker containers and this can take a while to stop and start. For the website though we run uWSGIs in forked mode, so it's only one container per host. This will probably change in the future, we're evaluating Mesos + Marathon for a more PaaS-like deployment where we can say "14 web processes please!"

Hope that answers your question.