2002 chevy avanalanche - low beam dont work always

ok when push the lever forward the high beams don't stay on ? then that lever should be replaced cause that's ur dimmer switch to switch between high/low beam lights if the lever is bad can surge you headlight and blow the headlights, have you check headlight bulbs its rare but it has happened that both blow at the same time

Replacement bulbs aren't very much money - replace one and see if it works. If they haven't been replaced since it was manufactured, it's probably time.

Light switch faulty looks like,

headlight relay or switch

I would start with checking the headlight bulbs (slim to none possibility but starting point) next go to the headlight switch.

You have a bad electrical connection. Check the wiring harness and both sides of it's connectors for corrosion and or breakage. The connector terminals will become worn and corroded and the wiring sheaths a prone to weathering and become brittle. Replace or clean as needed.

if you have power to both headlight plugs for each low and high beam filaments and the ground is good as you say the high beams function normally then you either have bad low beam bulb filaments,poor or dirty connection or you have a daytime running headlight relay on the car and that is the problem with the low beam lights.yes the high beams will work but not low beams if it is the relay.

If it's not the bulbs, be sure to check them, might be dual filament and the high beam wire is fine but the headlight one is shot, one bad wire would cause both headlights not to work.
Hopefully that's the problem, if not, it could be blown fuse/short in the wire. Try checking power/ground at the bulb to reduce the possible problems. If it has both with the headlights "on" then it's the bulb, if it's missing one then follow the wire for any irregularities.
They sometimes pass the wires under the flooring right near the drivers feet, which is a perfect place for water/salt to seep in and corrode wires.

The daytime running lights run the high beam bulbs at low voltage so it sounds like you need to put the relays back where they were and either replace the low beam bulbs or repair the wiring to them.Also the relay you removed could be defective.

it sounds like the actual lever is bad. looks like it is time to get it replaced