...make sure your players trace() function for gravity detects entities; make sure your lift is solid and has polygon set for detection.

The tricky part is getting your player to move slowly and rotate with the lift. After each "gravity trace" the player does, check if their is a lift entity under it, if so, then you'll have to calculate the lifts difference in position and rotation from the last frame and add it to the entities position. Tip: vec_rotate();