I just got anxiety looking at those pictures and how you got so close to those uncovered sheeves and fly wheel.
Those need to be covered, your building management need to get this lift properly maintained by a elevator company service provider.

The clunking youre hearing is the brake, which can be adjusted so it is less noisy (your cheapest option)

Obviously you can install sound proofing.

My biggest concern is how everything is uncovered and I hope the lift was switched off before you got near the machine (not engine)