The two flats (there were only two to begin with, the rest of the ring is circular) are still in good shape. The vise I have is very old, it belonged to my great-grandfather. Maybe that's why it won't hold the lock ring in there very straight.

I think I will try visiting the LBS. If they can get the lock ring off, then I am good and can finish the rest of the work on my bike.

Thanks for the help.