Left hand thread lug nuts on driver side

I wouldn't drill anything other than broken off flush and don't drill through. A blind hole will give you a surface to push against.
Even then, I'd go with a big C clamp first, but I have a good selection. Put a socket over the head and clamp down from the other side. You can wack the screw end of the clamp, then tighten some more....they'll come out.
To get the new ones in, I line up the splines best possible and draw it in with the lug nut. You may want to stack washers behind the nut to get by the non-threaded area, washers also makes a slip surface so you don't mar the surface