Explore everywhere.
There is a key on the first floor to open the locked door on the second floor to get to the lever handle. IIRC the key is on a desk where you first meet the demon (who then runs away) at the south east part of the map.
Once you repair the lever, you need to stand inside the elevator to activate the levers on the outside (I assumed they were the usual 'call elevator' mechanism at first).
