And people in the academic world have implemented live migration for just plain Linux processes as well. But when you migrate at that level you run into issues with things like open files and open sockets that are not easy to solve.
LXC is mainly a way to manage multifunction servers in a clean way, and Docker is a nice tool to help you leverage LXC without having to learn all the details. The nicest thing about Docker is that a developer on Windows could set up a VirtualBox VM with Linux, run all the same Docker Scripts as the production server, and have a reasonable facsimile of production to do testing.