Both are possible. And since docker itself is not yet production-ready, exporting docker containers to "inert" server images (for example AMIs) is a good stopgap which allows you to use docker for dev and test.
But that is not the ideal workflow. The ideal workflow is to run docker on all your machines, from development to production, and move containers across them. If you don't do that, you will miss out on a big part of the value of docker. To name a few: identical images in dev and prod; lightweight deployment; and a toolchain that is less dependent on a particular infrastructure.
This is something very interesting and under-communicated. I've always assumed docker is run on the production server and is used to pull updated images and spawn containers. But you're suggesting one uses custom toolchain for making an image out of the container filesystem and the LXC template, and then deploy this container?