> How about this one: as lift works perpendicular to the wing right?
Well err no. There is no such thing as a single lift vector..
Sum ALL the force vectors acting on the wing and you get ONE vector pointing upwards and backwards. You can split this into two orthogonal (right angles) vectors pointing in any direction you like...
But for convenience it makes sense to choose one pointing upwards at right angles to the airflow because weight normally acts downwards, also at right angles to the airflow (unless you happen to be wave or ridge soaring etc).
You could define your lift vector to act perpendicular to the wing but you don't have to.