Since the car is still under warranty, I would let your Lexus dealer check out the alarm system.....that is definitely something that has to be professionally checked out.
This is the first post that I've read about this type of problem, but to answer your questions, yes, it can be disconnected, and no, the factory system doesn't use motion sensors, so sensitivity does not fit into this equation. Yes, the alarm will shut off after about 3 minutes.