So sorry that you lost your lamb, it's always so sad.
You can either call your local hunt kennels (if you have one) or the company that picks up fallen stock in your area. The slaughter-man has never asked for any paperwork when he's picked up from me, I've just put it in my stock records.
I've never used another farm to get rid of fallen stock, so don't know what should be done paperwork wise in that situation.