Hello Elizabeth,
Sorry to hear about the lamb, badgers will eat lambs in fact they will eat just about anything. Their normal diet is however worms and grubs. I have never seen badgers actively go out to kill a lamb , but I know they will take carrion or maybe even go for a very weak or injured lamb. Foxes are the most likely culprits I would have thought though . Foxes will do this sort of thing all the time , a badger would only do it on rare occasions . Some people I knew years ago had a problem with badgers killing their chickens, I however had a badger set very close to my chicken/ducks/geese etc , had no problem at all , in fact I saw the badgers walking among the chickens etc on more than one occasion . The chickens took no notice at all . Maybe I was just very lucky ?, the only sure way to find out would be to put the dead lamb back , and stay up and watch to see what comes to collect it . Motion activated cctv's are quite cheap now , so you could set up one of those to see what you have walking around after dark, most of them work perfectly well in the dark . Hope you find out what it was, and good luck in the future.
cheers
Russ