Of course, in the olden days
lamb's tails were just 'docked' i.e. cut off
Nowadays the farmer/shepherd applies a special very tight rubber band which cuts off the blood supply and over a few days the tail withers and drops off ... the lambs really don't seem at all bothered by this ... when we had the smallholding I was trained to apply the bands for this and for castration, and I attended to this with our lambs ... I can promise you there was no bleating or signs of distress, absolutely none ... I wouldn't have done it if there had been.
Somewhere I have a Certificate in Lambing and Castration! That used to focus minds in Social Services appraisal interviews
However, of course removing the tails in this way means that they're not available (nor suitable) for the kitchen.