Dating myself a little, but LXC came along well before runc. It predates Docker, and was actually wrapped by the first versions of Docker. I learned about LXC, and used it, after doing some research on how to build my own PaaS at work (pre-Docker) and reading that Heroku was using LXC for their platform. It worked decently for me, but required more in-depth knowledge of all the knobs for disk mounts and networking than Docker typically requires.

You may be right that LXC has switched over to runc since then. I haven't kept up. I would be surprised though.