Just to follow up on my posting from a few months ago:
The LXD folks now have nested containers working (docker or lxc inside lxc)
https://www.stgraber.org/2016/04/13/lxd-2-0-docker-in-lxd-712/
https://insights.ubuntu.com/2016/04/15/lxd-2-0-lxd-in-lxd-812/
There was a dependency on cgroup...