SR9, excellent question. Normally I would make the answer to this question overly complex, so this time I will not mention vortices (darn, I just did!). So, as long as you just accept that the lip creates side forces, that will suffice.
The width of the lip controls the speed of the action or side to side motion. The wider the lip, the slower the speed. The forces on the lip also cause roll. The wider the lip, the more roll is generated. There comes a point when the roll becomes too much and the bait will spiral or swim on its side and become unstable.
The length of the lip determines the power of the forces. These forces are balanced by the water forces on the body of the lure. A good analogy is a see-saw, were the balance point is the tow eye. On one side you have the lip forces, the other the body forces. If the lip forces are too strong, then the lip is pushed down. It will reach a point were it gets too far down and it will break out to the side and spiral.
This is why on deep diving lips, the tow eye is usually on the lip itself, so that part of the lip force is above the eye, helping to balance with the body. Fine adjustment of this position will get you the maximum depth.
As for the various shapes and patterns of lips, I can