If you really mean LXC (see also: Comparing LXD vs. LXC) that might be more difficult (but maybe also not 
, see below) , but for LXD there are solutions:
https://blog.simos.info/discussion-on-running-x11-applications-from-within-lxd-system-containers/
If you are really using LXC:
- The above methods might be modifyable for LXC, but that might be more complicated.
- You might consider switching to LXD, as Juju can also use LXD: https://juju.is/docs/lxd-cloud