LXD is a management tool for LXC. More here https://linuxcontainers.org/lxd/
LXD image is an archive comprising of rootfs and metadat.yaml
https://github.com/lxc/lxd/blob/master/specs/image-handling.md
If you have time you have to try this:
https://linuxcontainers.org/lxd/try-it/
So what needs to be done is something along these lines.
Take stage3 extract it inside rootfs, generate metadata.yaml and compress it all (rootfs + metadata.yaml) in a new archive. (unified archive)
or
generate metadata and compress it to a new archive and use the stage3 archive as the root. (split archives)

metadata.yaml looks like this

architecture: x86_64
creation_date: 1454681520
properties: 
  architecture: x86_64
  description: "Funtoo current x86_64 (pure64) (20160205)"
  name: funtoo-current-x86_64-pure64-20160205
  os: funtoo
  release: current
  variant: pure64
templates: 
  /etc/conf.d/hostname: 
    template: hostname.tpl
    when: 
      - create

{{ container.name }}