Hello,
I have a 2012 Mini Cooper Countryman S. I brought the car used and the key or wrench for the lug nuts did not come with the vehicle I guess because it was broken off in the lock. If anyone has any suggestions as to how I might be able to get the broken piece out of the lock, I would be so grateful.

 

So you have a keyed lug nut?

A tire shop could over torque and break the lug and then put a new bolt in.