I saw an Electric Jen video where she taught her AP1 car to ignore the lip and park itself. I believe as long as the lip is <.5" tall it should do it.
I have to play around with it more tomorrow when it's not raining. My lip is definitely shorter than .5 inches so I am not sure that is even the issue, but it's the only thing I can think of that would be causing the inconsistency. I will video tape it tomorrow to show you guys.