How do I get this lag bolt out?
Left hand drill bit and bolt extractor.  

The idea being you drill a hole in the center of your lag screw shaft, drilling in a counter clockwise direction which will avoid driving the shaft in deeper, once you have your hole in the shaft you use the extractor again in a counter clockwise direction which threads the extractor into the bolt shaft and the drill in counter clockwise motion tries to remove it.

That said I'd sooner go the holesaw route and epoxy a same size wood dowel back in the hole.