I see three batteries X 1.5V, so 4.5 volts max.
The xAC V2 specs are 9-12V.
The xAC V1 specs are 9-15V. But, I got it to work as low as 4.3V when I was pushing the limits for a different issue.
I don’t think I’d recommend running it like that, but you could mount a larger 12v battery pack, then use a voltage regulator to drop the power down to 4.5 for the door lock.
Running the xAC continously will run your batteries down. I did a project that ran into the same issues. Read through it and you’ll see there were alot of ways discussed how to prevent constant power drain.
If you wanna try messing with the lock, then think of the xAC as just a simple switch. Once you get rid of the RFID that’s all it really is. You could figure out your lock by just jumping two wires with a paperclip. That should let you figure out where you need to tap into it at.