I think it is interesting that in Matthew's account of the lost sheep (chapter 18), it is just before the instruction about correcting the lost in the church. That ends in severe action. In Luke's account (chapter 15), it comes as an admonition to the grumbling of the Pharisees. Luke said that "he lays it on his shoulders." Again, I cannot be adamant about the matter. It is an illustration that makes the point that sometimes Jesus as the good shepherd has to be severe with us.Roy Gustafson, who has led many parties to Israel, tells in his book "In His hand" (p.46) that on one of his visits, on the road down from Jerusalem through the Judean wilderness to Jericho, they met a shepherd carrying one of his sheep with a splint and a bandage on its leg.
Said their guide, who'd lived nearly fifty years in that area, "The shepherd broke that sheep's leg himself."
And it was true! It was explained that this was a sheep that was always wandering off, and in the process leading other sheep astray. Membership in the flock carries certain responsibilities, and much as the shepherd feels a real affection for his animals, discipline is the only thing that will keep them together, as they must be kept together for their well-being and their safety.
So to cure this sheep of its self-willed ways, the shepherd had broken its leg, and then hand fed and carried it till the bone was mended ... and (hopefully) its waywardness.