Hello! This is only a guess, but I see this alot in the Grand Prix's, LaCrosses and some of the trucks that use the same setup. The low beam bulbs are powered up by a tiny module in the Underhood Fuse Panel, called an "HDM". Its item #35 in the fuse panel. It controls only the low beams, which is why the high beams still work. Its shaped like a relay, but isn't like the other relays, so you can't swap it out with another relay, you need another HDM for it.
Please let me know if you need additional assistance!