LXC is not on immediate roadmap but is very much doable since it is supported by libvirt which we already use. You can open an issue on our Github to track its progress, no promises though. :)
Docker works with LXC
used to. Now-a-days it uses libcontainer.
Docker moved out of lxc long time ago
Docker by default uses their own libcontainer now but you can change that. In fact last time I checked it supported quite a few via execution drivers like OpenVZ, systemd-nspawn, libvirt-lxc, libvirt-sandbox, qemu/kvm, BSD Jails, Solaris Zones, chroot