The lap in the reinforcing plies of a tire is designed to get tightened by the major rotational force of the position it is in. You want the outermost layer to be brushed in a direction that would just roll across the stackup dry, not try to snag the edge of the top layer and roll it backward. A rear tire's primary load is in power application, a front tire's primary load is in front braking application. The front tire used on the rear must be turned backward to maintain this relationship. The only exception are "universal" designs (usually no higher than an "S" speed rating, and very limited sizes) or a jointless construction tire. The lap joint is also, incidentally, where the heaviest point in the tire is. The next time you have a new bias ply tire, check the inner carcass opposite of the balance dot, and you usually find the bump and overlap that identifies the joint location.
I have a Michelin Commander rear tire turned backward on the front of my Road Star right now with 14K miles on it, and I'm thinking of flipping it around and sticking it on the back of my XS.
The direction of the tread on a motorcycle tire has very little to do with how it grips and handles. Tread grooves have one primary mission- to pump water out from under the tire. The tire does not care where it goes, and the direction of travel is not important, it just pushes the water sideways, or gives it a wide and deep enough channel to occupy for a short period of time to allow the tire to contact the ground. Tread grooves and block patterns have a secondary function of dissipating heat by adding surface area. Although the bulk of the carcass heat is transmitted to the sidewall and on to the wheel (bet you never thought your wheel was a heat sink, did ya?) the tread block itself is cooled primarily by the tread block surface in the wind. This is one of the reasons tires seem to accelerate in wear very rapidly if you continue to run them after they hit the wear bar. That, plus they are generally cooked at this point, and they shear material under acceleration, turning, and braking loads, rather than momentarily compressing into the irregular surface of the road and bouncing back.
These various descriptions are courtesy of Avon, Michelin, and Goodyear over several years and a certification or 3.