If it was your own lamb you could put a bucket on its head for a few days, lampshade effect,
Hopefully you mean one of those things they put on dogs at the vet - nice and lightweight, unlike a bucket (presumably you mean with the bottom cut out, but would be sharp and heavy). However, could the lamb still feed with something large enough to stop it getting its head through?
Soays are forever getting their heads stuck through sheep mesh, caught by their growing horns. Could you keep your cade somewhere different until its head is too big to fit through the wire? It's the 'grass is greener on the other side' syndrome