Removing a broken lag bolt in treated wood is one of those moments a Do-It-Yourselfer dreads. How a lag bolt broke off in the wood isn't important; what's important is getting it out of the wood safely, and without marring the wood. If enough of the bolt is still above the surface, you may be able to extract it with a pair of locking pliers or reversible drill. Otherwise, you might need an screw extractor.
Sheared Above the Surface
If 3/8 inch of the shank is above the surface of the board, you may be able to lock the chuck of a reversible drill onto the protruding portion. Set the drill to reverse and loosen the bolt slowly. The key will be getting the drill chuck to grip tightly enough. Often, you can get a tighter grip with locking pliers.
Measure the shaft to see if at least 1/4 inch of it is above the surface. If it is, you can use a pair of locking pliers to remove the bolt.
Lock the pliers in place around the shaft of the bolt. You'll need to adjust a small knob on the end of the pliers to get it to lock tightly. Try to lock the pliers parallel to the treated wood; you'll generate more torque and have fewer turns to get the bolt out. If that's not possible, lock the pliers at as close to parallel as you can.
Rotate the locked pliers counterclockwise until the bolt comes out. If the pliers slip off during the removal process, just reattach them to the lag bolt. You might find it easier to reposition the pliers closer to the wood as the bolt comes out.
Sheared at or Below the Surface
Mark the center of the broken lag bolt with a center punch and hammer. This hole is needed to get the drill bit started.
Drill a hole about 1/2 inch deep into the shank of the lag bolt with a carbide-tipped drill bit. Your extractor bit may have special instructions on how deep to drill the hole.
Screw the extractor bit into the hole. Extractor bits screw in counterclockwise.
Grip the extractor with a pair of locking pliers or a tap wrench. If you use locking pliers, position them parallel to the wood. Turn the extractor counter clockwise until the bolt comes out.