A rethreading tap and die can be very handy. First, I would question anyone who would cross thread a lug nut as it shouldn’t really happen but it does. The rethreaders will clean up the problem without taking out a lot of metal. The damage has always seemed in the first 4 or 5 threads with no damage in the threads that get the torque. But if the stud is available replacenent is certainly preferred and the shop shouldn’t quibble over it.