Copy lxd containers between hosts

The later release (non-beta) of lxd (v2.0) seems to have resolved my issue. The steps, which may be found in the excellent documentation here, are:

1. Publish an image (without stopping the container) on host A;

   $ lxc publish --force container_name --alias image_name
   Container published with fingerprint: d2fd708361...a125d0d5885
   

2. Export the image to a file;

   $ lxc image export image_name 
   Output is in dd2fd708361...a125d0d5885.tar.gz
   

3. Copy the file to host B, and import;

   $ lxc image import dd2fd708361...a125d0d5885.tar.gz --alias image_name
   Transferring image: 100%
   

4. Launch the container (from the image) on host B;

   $ lxc launch image_name container_name
   Creating container_name
   Starting container_name
   

In some instances the publish command may lead to a split xz tar-ball --- but both formats are supported. Simply import the meta-data and rootfs components with

    lxc image import <metadata tarball> <rootfs tarball> --alias image_name

0_0 posted a good answer but I'm not allowed to comment just yet so I will just post his answer modified.

First off lxc publish --force container_name --alias image_name will stop the container and restart it but the OP did not want the container to be stopped.

You should make a snapshot first with lxc snapshot container_name snapshot_name

Then you can publish the image with lxc publish container_name/snapshot_name --alias image_name

Now just follow the rest of his instructions.