Adding Authorized Keys to the LXD Default Profile

Adding your key is as simple as:

$ lxc profile edit default

You will then need to modify the contents from:

config: {}

to:

config:
  user.user-data: |
    #cloud-config
    ssh_authorized_keys:
      - ssh-rsa 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 ssh key

Where the ssh_authorized_key is your public key, probably identified by cat ~/.ssh/id_rsa.pub.