My low beam headlights won't turn off when the car is off?

check for power and grounds at the headlight plug for both lights as you could have 2 burnt out lights, have had this happen a few times. you don`t say if its just the low beams. there are 3 wires one is the ground one is low beam and one is high beam. it could also be the headlight switch that is bad on the headlight circuit only. have had this happen twice. you would have to remove the switch from the dash to gain access to the plug connector to test the wires coming out of the switch, for the headlights. a third thing is it could be the dimmer switch that is bad. myself I would check the dimmer switch first then the headlight plug at the lights then the switch for the headlights.

It happened to me, both low beam filaments in both new at same time (happens a lot so I'm told) The earths are in a stoopid place under the left headlight.

Have you checked to see if the bulbs are burnt out or if the low beam fuses are Blown?

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

It's the headlamp relay #46. If you want to test it, swap it out with the cooling fan relay #45 and see if your headlights work. If they do you know this is the fix. Found the solution online a couple of years ago and it was spot-on. The part was $45 at autozone at the time.

it s the headlight switch or headlight module

Sounds like a faulty headlight switch

Is there a fuse on low beams? Check for that and power reaching the lamp assemblies. Grounds? Connections? New sensor?

try the lights with the tilt wheel in the up position. If the low beam works then, a wire has pulled out of the connector on the mutipurpose switch inside the steering column. remove the covers behind the steering wheel on the column and there is a large multi wire plug with many wires. it should be obvious which wire has pulled out or broken.

Could be the relay for the lowbeams is faulty, if your DRL's are your lowbeams, then your DRL Unit could be bad. Also did you blow a fuse cuz a random surge could blow the fuse

Have you tried new bulbs, its rare but both low beams may have blown at the same time, it has happened to me in the past.
I don't know your car but the high and low beams could be fused separately so you are left with at least one set in an emergency.