Indeed, LXD would seem to be a faster, more efficient way of doing what you would do with traditional VMs. I don't see a lot of overlap with docker, despite the superficial similarity.
The security around the containers still isn't as good as a hardware VM, but I think hardware segregation is on the road map.
It's ideal for running container inside VMs, though, and offers nice management segregation on those larger VMs.
However, the development of Zones and Jails (on SunOS/Solaris/illumos and FreeBSD) was much more security focused, with the default being "that's not allowed in a (Jail|Zone) until we can make sure it's safe". I really wish Linux had just ported Jails or inspired their security model on them.
I do a lot of work with the internals of Docker and runC at SUSE. Trust me, it's not pretty how you have to set up "Linux containers" and there's 1001 gotchas.