No sheep or lamb can ever qualify as a 'pet' in the eyes of the law, it is very clear on this. So to stay within the law, you need to get it taken away by the knacker/fallen stock. Really vet should not be encouraging breaking the law......
The only exception and then only for the UK is for pet horses (tho not working horses) who because they are essentially not in the UK food chain have a part derogation allowing burial where is is well away from water courses, well draining ground etc.
But lamb, no, that has to go to the fallen stock people. Lambs are a cheap fee too, so cost not really an issue.