Apples to oranges. LXC can be directly compared with a small, and quite insignificant, part of Docker: container runtime. Docker became popular not because it can run containers, many tools before Docker could do that (LXC included). Docker became popular because it allows one to build, publish and then consume containers.
> Docker became popular because it allows one to build, publish and then consume containers. True, but Docker is an awful choice for those things (builds are performed "inside out" and aren't reproducible, publishing produces unauditable binary-blobs, consumption bypasses cryptographic security by fetching "latest" tags, etc.)
Docker supports multi-stage builds. They are quite powerful and allow you go beyond the "inside out" model (which still works fine for many use cases).
> ...and aren't reproducible
You can have reproducible builds with Docker. But Docker does not require your build to be reproducible. This allowed it to be widely adopted, because it meets users where they are. You can switch your imperfect build to Docker now, and gradually improve it over time.
This is a pragmatic approach which in the long run improves the state of the art more than a purist approach.