How do you remove a broken lock lug nut?

Lug bolts are normally hammered or drawn into place with the use of the wheel. They are removed the same. Remove the wheel, you may have to set the rotor in such a position that allows for the lug removal. Usually a very small gap allows for it. Take a good hammer and carefully pound it in till it pops out the back. Take your new one and push it in than tap it a few times till enough thread is showing that it can be drawn in all the way with the wheel installed.