When he said a lift, I assume he meant an elevator. Even though an elevator isn’t technically operated by a level, and instead by a pulley, the phrase “a lift takes a lever” has better alliteration with two words that start with the letter ‘L’. So the man most likely was intending to make a point about how even though we don’t see it or appreciate it, the elevator has something doing the work for it.
If he was talking about a car ride (which is what I first thought, although now that I’m reading the question again it seems like it’s just an elevator), that man was probably using the word ‘lift’ for both the elevator and the ride he was about to take—insinuating that the ride is like an elevator, as while it gets you to where you need to go, we sometimes don’t appreciate the effort made to get there. This would have been him recognizing the effort being made by who was driving him. If it’s just an elevator he’s waiting for, it was probably just him recognizing the hard work that goes behind the mechanics of an elevator.