I'm a little surprised that lxd doesn't cater more to nfs rather than bind mounts etc for file sharing. I mean if you already have private/secure networking - just use a network filesystem for your... Network filesystem needs?
There are patches floating around (similar to the work we did to allow FUSE) but they haven't made it upstream yet and my understanding is that there is some tricky corner cases on NFSv3 which still need to be sorted (NFSv4 was easier due to already having uid mapping capabilities).