Okay, here is the concept: We have a chain of 6 repeaters, connected to a latch so that we can control what floor the lift is on. The bottom sticky piston is connected to both 1st and 6th repeater (isolated), the middle is to 2nd and 5th and the top one is connected to 3rd and 4th.
But that is not all. If we do not do the next step, the top piston will not go down.
To fix that, we need to connect a special part to the 3rd repeater (or one of your choice, just make sure the timing is right). The special part consists of a delay which delays for the time needed for all pistons to contract and this:
Input
├→I┐
└─→│
Output
I┐ is an inverter.
Connect input to the delay sequence and inverted ouput to the middle piston.
But that is not all. If we do not do the next step, the top piston will not go down.
To fix that, we need to connect a special part to the 3rd repeater (or one of your choice, just make sure the timing is right). The special part consists of a delay which delays for the time needed for all pistons to contract and this:
Input
├→I┐
└─→│
Output
I┐ is an inverter.
Connect input to the delay sequence and inverted ouput to the middle piston.
Voila, it should work.