I had the same problem last week, it took ages to get mine off.
What i did was drill straight down the centre of the stud, with a drill piece almost the same size as the stud, then chiselled as much of the lock nut away as possible, then i jacked the car up and pulled and shook on the rim, then eventually it loosened itself.
After spending days and nights on doing this, cutting up my hands and putting minor scratches on the rim trying to work out ways to get the piece of shit off, i was sitting in the car just looking through stuff and yep you guessed it.......The lock nut key was in the centre console the whole time. Ah well
oh yeah my lock nut is the same style as yours too.