Does anyone here know how to lasso?  I have a lasso, and I can do a few basic tricks; flat loops, etc.  But I was wondering if anyone knew anything about this particular piece of equipment?

Wow.  Where was the ranch?
I believe the various technical terms you are looking for are honda (the knot) and spoke (the left over section that you hold).  My lasso has a proper knot, known as the honda knot, instead of the leather covered rope, and I believe both are acceptable.  In fact, the honda knot is known as the cowboy knot too, and the name honda knot was given because it was used as the honda.  Or maybe the other way around.
The only twirling I do is to create the loop for the flat loop, and then throw it.  The thing is, over twirling it can cause it to become kinked, and so there will no longer be a loop left, merely a collection of kinked sections.  Anyways, looping someone at 10-15 feet is good, because my rope is only 16 feet long.  So at fifteen feet, I would only have a foot circumference loop.  Not going to loop much with that.
Also, the wrist flick is probably not as difficult as it sounds.  You merely send a wave along the spoke, which carries the honda further along, tightening, of course, the noose.  I think also that having a noose too big will cause it to be able to land on someone's feet rather than loop them around the waist.   I have looped someone only once before; around the waist, first time, at a stupidly easy distance of five feet.