Basically dragging the target. The standard tangle DC is 10+Spell Level and Escape Artist check is only 15... but would the DC for both raise on a successful Ride-By Attack? What would it be? Also what damage could be assumed?
Unless they've covered this in one of the little splat-books I haven't read, I know of no rules to govern this situation.
Real world physics: No cowboy would do this, not even to a hated enemy. It absolutely would yank the cowboy out of his saddle, guaranteed, unless he lashed the rope to his saddle horn (that's why western saddles have saddle horns). Assuming he does this, he runs the risk of breaking his rope, breaking his saddle, and injuring his horse. All of which are very possible.
If a real world cowboy wanted to do this, he would stop, lasso his target, then slowly accelerate until he was dragging the victim.
I've never tested this myself, but I think a person can survive for quite a while being dragged over typical ground. Even a normal commoner with 5 HP would survive for a few minutes, so even doing 1 HP per round would probably be too much, realistically.
But that's no fun. Pathfinder has magic, we don't need real world physics.
I might go for something like 1d3 non-lethal damage per round. I would definitely require the rope to be fastened to the saddle rather than held. I would not allow the dragging to begin until the following round (representing at least slowing the horse down, before or immediately after lassoing the victim, then accelerating the following round). I also would not allow it for any victim unless he is a size smaller than the rider's mount (large horse to drag medium or smaller victims).
I would not adjust the DC because of the ride-by attack. Being entangled, and the next round prone, is bad enough, especially with no real risk to the rider using the lasso. Heck, a first level commoner could literally kill a heavily armored high-level fighter, if that fighter had no ranks in Escape Artist and no slashing weapon, without ever even taking a scratch himself - as long as he could hit with his lasso in the first place. It would take a while, but would be unstoppable. OK, well, a high level fighter probably has at last a 16 STR so he could eventually break the lasso before dying, so let's say a mid-level fighter instead - with bad rolls, he might be unconscious before he breaks the lasso and even if not, maybe the rider has more lassos...