So? OMG I can't make this character as one specific class! The world is coming to an end! We must change the rules!
That was my first thought too, though with way less snark. No, the Pathfinder ruleset cannot make an exact copy of every sort of character in history or fiction, and from my perspective, that's a feature rather than a bug. Games are defined as much by their limits as their possibilities. I mean I'd love to play a game of chess where I could win by just hurling expired produce at my opponent until s/he concedes, but that might detract somewhat from the nuances of chess.
Monks are lawful because they are created in monasteries. If you abide from a code you get from an organisaiton without, rather than within your own principles, then you're lawful.
It's also basically tradiion handed down through four editions of the game. The man you really need to ask that question will need to be reached via a Ouija board or seance.
I agree with your second statement much more than your first. You could easily have a monastic tradition of rogues, fighters, wizards, even barbarians if you wanted to stretch the concept, but that doesn't imply they'd all be lawful. Most of them? Sure, but there's always outliers.