Sorry to hear that you lost a lamb; it's always upsetting, no matter how many you rear for how many years.
If you do have a collector that can pick up a single dead lamb for a few pounds, all well and good - but otherwise, if the farmer you got them from is nearby, I think I would be tempted to ask him if you could pop it into his dead lamb sack - if it's the same where you are as here, he will have them taken away in sackfuls and will pay by the kilo. (Gruesome I know, but the sad facts are that you get lambs born dead and young lambs that die.)
As a commercial farmer that sometimes sells orphans to local people who I think will be sensible and look after them ok, I would hope that your vendor will at least dispose of the carcase for you if not offer you a replacement or your money back. Orphan lambs do not all survive, but they really should get through their first 24 hours in a new home if they were fit and well when sold.