Murder on the Zenith Express: the Gordon Mamon collection (Paperback) (ISBN-13: 9780648322887)

Gordon Mamon was the lift operator in a hotel that didn't have a lift.
The hotel, the 'Skyward Suites 270', was the lift.

All Gordon wants to do, when he isn't delivering room service, administering first aid, washing dishes, cleaning bathrooms, or forwarding service complaints, is to be able to finish his crossword in piece. But people keep inconsiderately dying of unnatural causes during their stay aboard his lift-module on the Skyward space elevator.
Welcome to Module 270, an orbit-transiting hotel with a suspiciously high body count.