lxd-tramp.el offers a TRAMP method for LXD containers.

It uses lxc command line tool to login to containers and list running containers (for completion purpose).

Offers the TRAMP method lxd to access running containers

C-x C-f /lxd:user@container:/path/to/file

where
  user           is the user that you want to use (optional)
  container      is the id or name of the container

Thanks to montag451 the author of lxc-tramp.el for suggestions.