In case anyone else wants to know, it works like this:
~ unregistering an Arturia product does *not* unregister your ownership of the associated Ableton Live Lite (ALL) licence.
~ You can keep using ALL once you've sold or given away your Arturia hardware if you want to.
~ If you want to unregister the ALL licence with Ableton, you can only do so by transferring the ALL licence to another person using your own Ableton account on the Ableton website
~ If you want to do that, the new owner of the licence has to register with Ableton themselves*first* & then tell you the email address with which they registered, and then you have to tell Ableton to transfer the licence to the new owner, giving Ableton the email address of the new owner.
~ You can, so far as I can tell, sell the ALL licence, if you can find someone silly enough to buy it.
Hope this helps someone else.