LXC is a bit more simple than that; the modus-operandi is to unpack the rootfs of your favorite distro (ie, ubuntu, alpine) into the container and it runs /bin/init in that container. It essentially behaves like a full VM without the virtualization part.

Tooling would be things like Ansible to setup the container as if you would a normal linux system. Though to be honest, not many people invested in good tooling around LXC, it should be possible without problem to run a docker rootfs in LXC.