I have no experience with lambs but in dogs and cats you would pass a urinary catheter. I wouldn't have thought cutting the end off of his willy would have sorted it as the blockage may be further along the urinary tract. You can get back flow of urine to the kidneys that can cause kidney damage so prompt action required, A large gauge sterile needle into the bladder would work to relieve pressure. Hope all is now sorted out for the poor chap
Yes I don't know how it works but it was a vet who told me. It's not the whole end of the penis, just the very narrow bit at the tip. If he's not for breeding then apparently that wouldn't cause him much of a problem, but if he was intended for breeding.....well, you wouldn't use him anyway in case a tendency to urinary calculi is inherited, but I would imagine it would prevent him depositing sperm far enough up.
I think it's an emergency measure to prevent the bladder bursting, if there is no access to a vet or to equipment or skills such as passing a needle or urinary catheter (who has a sheep sized catheter kicking about?). Yes the blockage might be further back up the system, but it might not. I can't imagine having to do that though