We produce the signed invoice (proving the node gave the invoice), and the pre image (proving it was paid). It also contains the (made up) key of the person who requested the invoice. We now need to sign something transient with that key to show we own it. I think it needs to be a simple string, because there are many cases: 

1. I might want to link it to my nostr/Twitter handle or wherever I'm publishing my proof. 
2. I might want to link it to my real name.
3. I might want to link it to a block hash to prove it was after some time? Then I can time-stamp pincer with opentimestamps to prove a time range of creation.
4. I may just want to attach a random snarky comment.