Hello and welcome to Just Answer!
There is one simple test you can do to try to determine what is goin on. After that you are gonna have to get into some pretty difficult wire chasing.
with the low beam headlights turned on check for power to fuse 3 and 4 in the diagram. these are the right front and left front low beam fuses. If you have power, then your problem is between the fuses and the headlights themselves. If no power, replace the low beam relay (GM calls this the Headlamp Driver Module- its just a relay). It's item 35 in the photo.
This relay is different than the other relays so don't try to swap it with anything else to see if it works. This is a high failure rate part and is available from GM. Make sure you call it by it's real name, the headlight driver module.
For any other troubleshooting it will be necessary to have a scan tool with body computer communication capabilities.
I hope this helps. If so please press ACCEPT for my work. Let me know if you need anything else.
ASE Certified Technician
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