OMG!! Lug nut is completly stripped !!!!

Take a small drill bit to the back of the stud right in the center to use as guide. You just have to do a shallow hole. Get a grill bit one size larger then the front of the stud. Drill till the head pops off. It will be easy to do if you in bolt the hub and take the whole thing off.
 
You need to remove the hub from the axle.

You can use a wheel to remove the head of the stud.

Just be careful that do not bite too deep into the hub, as you will be working at an awkward angle.
 
Whatever way you have to remove the head of the stud without damaging the hub. If you can get down to it with a grinder, that will probably allot quicker than drilling it. You can pull the hub off by taking the axle nut off and sliding it the axle, it should make it easier to get to.