Low beam headlights not working

If there is no power to either of the low beam fuses either the relay for them has failed or it's control signal isn't operating. To determine if it is the relay or the signal from the BCM you will need to go to the fuse block under the hood on the left side. Unbolt it and find connector C2 a 30 pin brown connector. In it you need to find a Pink wire with a white stripe on terminal number 18. This is the control signal for the relay. If you push a pin into the back of the wire and apply a wire connected to a ground to it the low beams should come on if the relay is good. If they come on then there is an issue in that wire as it goes to the body control module or the module itself. If the lights do not come on when ground is applied the relay has failed. The relay is soldered to the circuit board inside the fuse block. There are two ways to repair it. Replace the fuse box with a new one or wire in an external relay.

HMM. That makes it sound like the BCM is acting up. When the ABS light came on did anything else happen? I know there are a couple makes that have issues with some of the scan tools out there, but haven't heard of anything on the Equinox. What scan tool did you use to reset the ABS light?
Good that a reset fixed it, just wondering what item turned it off to begin with.

I would try gently tapping the fuse box with the low beams on and see if they flicker or go out as well. The low and high beams share the ground connection. If the high beams work but not the low beams it is likely on the power feed side. If both are a problem then go after the ground connection. GM has had many issues with the relays going bad, but they have had a lot of ground issues as well.