I'm leaving this here in the hopes that it makes it into search engines, that's also why I mention a character name for SEO... This just cost me over an hour of troubleshooting.

If you get into the underground in Book 3 and have to operate security gates but the lever will not stay down to let Hannah through, make sure you do not have any game controllers that are not gamepads attached to the computer! Exit the game, then disconnect any input but keyboard, mouse, and maybe a gamepad.

Especially any device with a non-centred axis, like flight pedals, can make ever-buggy Unity input handling fall over and break this "puzzle" by immediately releasing the lever and blocking progress.