Pretty sure that pressing 'E' in System Shock makes you lean. You're thinking of the mouselook mods, which give it a SS2-style "inventory mode" which is toggled with 'E'.
I read the question as "What was the first PC FPS that had Y-axis control using the mouse," which would, to my knowledge, be System Shock. And it is required to complete the game, since there are, amongst other things, security cameras on the ceilings that must be shot out to progress at some points. But if the question is "What was the first game with mouselook," it's probably Marathon.