"Depth is increased on all types of lips by the angle of the lip and the distance of the line tie from the tip of the lip. The larger the bill and the shallower the angle, relative to the horizontal centerline, the deeper the bait dives. "
Depth is increased only from the lip being longer. The longer the lip the deeper it goes. The angle controls two things. Wiggle and the ammount of time that it takes for the lure to reach maximum depth. The greater the angle the more wiggle a bait will have. A lip horizontal to the center line will dive steeper and achieve maximum depth quicker. Since the dive angle on a straight lip is steeper then the bait may achieve a little more depth. The main point here is that the bait will be on the bottom quicker and in the strike zone longer.
"Line ties closer to the baits body increase the potential for maximum diving capacity, the closer to the end of the lip the shallower the diving potential."
No. Line ties closer to the body increase the wiggle of the lure. It does not increase depth in the sense that you are looking for.
"Round lips cause a wide wobble and tend to cause the baits tail to swing back and forth. This is increased by adding to the width and the length."
Width, not length. It is true for all types of lips.
"Square lips cause a tighter side to side motion and less tail swing. They are also exceptional for pulling through brush."
No/Yes, The width and angle of the lip control the wiggle of a lure. They say that the square bill is exceptional for pulling through brush. But this is a myth. The short lip gets it through the brush. Round or square, it all works.
"What are the benefits of coffin lips? a cross between the two? "
Coffin lips will deflect better than round lips.
"Does the thickness of the lips have any major effect on a baits diving ability other than weight? "
Yes, The thicker the leading edge of a lip the more resistance the lure encounters reaching maximum depth. In other words, your bait will dive deeper and faster with a thinner lip.
"Are there any set rules for lip width relative to a baits width? "
No, It is trial and error.
"Or lip size and angle for desired depth of dive? "
Yes. You will gain (roughly!!!) 10 ft. of depth for every 1 inch of lip from the nose of the bait to the end of the lip. The straighter a lip is comming out of the nose of the lure the quicker it will achieve maximum depth.