Seeking advice on how to extract broken lug bolts

Try and keep it simple 1st. Use the correct size center punch to mark the broken bolt. If the surface of the broken bolt is too rough to center punch use the largest drill bit that will drop inside the bolt hole that is smaller than the hole thread I.D.. Use that bit to resurface the rough broken part of the stud. STOP when you have made a nice "divot" that will allow you to drill the center of the stud. This method will allow you to find the center of the broken stud without significantly damaging the outermost threads. By the looks of those holes this should not be a problem. Then use your mag drill to do what jos 7150 described. Some eazy outs are much better than others and can be used for this task. Make sure you drill all the way through the stud with you mag drill and that will increase your success rate. It will also allow you to spray penetrant thru the bolt which can penetrate back toward the broken stud head. The heat produced by drilling the stud can also help free it up and aid your removal.