Hmm, I fear I will be the devils advocate once again. I do not agree with the 'keep your dog on a lead at all times in fields of livestock' rule.
If you actually have control of your dog - and I don't just mean it accompanies you on a walk - there is no reason whatsoever that the dog needs to be on a lead at all, ever. Problem is, few of us have that relationship and can therefore trust our dogs that implicitly.
My dogs don't chase. They are simply not allow to. Lambs, pheasants, squirrels, cats, day old chicks. Not allowed. End of. The day any of mine hurt another animal, I will offer myself to you to throw sharpened sticks at.
I will use my disctretion to put them on a lead. If livestock seems very nervous, if other dog walkers put theirs on a lead, if a sign says 'keep your dog on a lead', if I need to rescue a stuck lamb I'll put them on leads in order to tie them up out of the way to simplify the job and prevent them helping (which is not always helpful at all!).
Otherwise I keep them at heel, trust them, and they respect me; the German Shepherd for different reasons than my 3.
Anyone however that does not have this kind of relationship, and especially (pet hate) anyone who cannot recall their dog must at all times keep it on a lead. Its just common sense at the end of the day (maybe that is the problem!). Dogs are like people; some are good and some need a little help to be good - and breed has an awful lot to do with how difficult that road will be. We shouldn't however assume they are all flesh tearing maniacs fighting to control an impulse to shred other animals to pieces.
However I'd never have a terrier! Or pitt bulls!
Big lamb died yesterday evening, too many wounds, poor thing. Did the best we could - thanks so much for all the advice. The dogs owners will pay for both lambs. The second one very quiet. Bloody irresponsible dog owners!