Mostly it is because of the size of your model. It's HUGE!

Given the size of the entity's bounding "egg", it is really easy for him to side off of the lift as it goes up. Even if he didn't side off, his head would hit the ledge above and push him through the lift.

Solution, set the lift to activate on a trigger. Put a trigger near the center of the lift with the same id and a small trigger range (I used 2).