Sorry about this; I experimented some problems with the Elevator on the Library.
But it actually works fine, you just need to follow this steps:

After pressing the button on the left to make the Elevator going up, you'll be in the upper area. Now just try to NOT jump off the place if the Elevator is still up.
If you go down that way, you'll never be able to go back up there. You need to get down by pressing the big Switch next to the Elevator. And if you want to go up again,
the little button will be not working anymore... but just place Lara next to it and the Elevator will move up again.

That's the right way to do it =)
