Filesystem hierachy for LXC unprivileged containers

I don’t want to place containers in /home but in the /var/lib space. Neither with a rare path like /var/lib/unprivilegedcontainers but in a more common style to match most of people.
I’m currently linking /home/lxc/.local/share/lxc to /var/lib/lxc but I see /var/lib/lxc as really only adequate for privileged containers, and with the risk of some hypervisor launches anything in /var/lib/lxc/* as root.

What is the best directory name/tree to design?

An example:

mkdir /var/lib/lxc.u
chmod u=rwX,go=rX /var/lib/lxc.u
mkdir /var/lib/lxc.u/john
chown john /var/lib/lxc.u/john
chmod u=rwX,g=rX,o= /var/lib/lxc.u/john
ln -s /var/lib/lxc.u/john /home/john/.local/share/lxc
mkdir /var/lib/lxc.u/maria
chown maria /var/lib/lxc.u/maria
chmod u=rwX,g=rX,o= /var/lib/lxc.u/maria
ln -s /var/lib/lxc.u/maria /home/maria/.local/share/lxc

(I really only use a single account for unprivileged containers, like “lxc” instead of John or Maria)