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It's the same for me - the app always shows the trunk is open. It also won't unlock the car, but it will show it as unlocked. It will, however, lock it if it is unlocked. I've owned the car less than two weeks and have discovered it's a pretty buggy app. But I still love my car.
I called Lexus and was told they are aware of the trunk lid open bug and are working to fix it. He couldn't help with the app not unlocking my car.
Edit: Now my app isn't remote starting or unlocking the car. I have to take it back to the dealer so they can check the DCM (data control module). Not a happy camper, I've owned the car less than two weeks.