I think Lunge is exactly right in suggesting that you try to put the hook in a place other than where the weight goes. What I typically do is once I have the lure blank I lay it out on the table in front of me and then lay the hooks down next to the lure as if they were attached. By doing this you can see where the hooks balance the bait best and also where they will give you the best chance for a solid hookup. Once you decide where the hooks go make a small mark in the wood, I use a nail to do this. Now you can figure your weight configuration around the hook placement locations.
All of that being said, I have put hook hangers straight into the lead without any problem whatsoever. I test each lure for proper weighting by placing the weight on the belly with a rubber band and floating it in the sink. Once I know exactly how much lead I need, I drill my holes being careful to watch out for the hook placement marks I mentioned above. Next melt the lead with a small propane torch, and pour the lead in. Finish off everything with the wood putty and seal the wood. Now you should be able to just drill right into the lead...if not, make sure the bit you are using is sharp and that the drill is turning the right direction, lol. Lead is quite soft and should give you no problems at all in drilling. Once the pilot hole is drilled the screw-eyes should go in like they do in the wood but a bit tighter.
Jed