The why: Your trap leg (the one that crosses) is to the outside of your opponent's hip. This gives you way more movement. If you trap with your inside leg (the one that is pressed down by your opponent) your movement is very limited. Try whipping up with your inside leg as the trap. Your opponent's weight is on that leg. Also, when you whip up to your side, if you have your inside leg as the trap, you are almost certain to lose the lockdown because your opponent will be moving to your right, and your trap foot (your left foot) is the only thing keeping him in lockdown. He'll simply move over it and smash you back down. Outside over, outside over, outside over.. just keep thinking outside over - drill drill drill drill drill drill... eventually you don't even think about it, you just do it. Work on your stomps - the best thing I did was go over the stomps at the Decatur seminar. Understanding HOW to get to lockdown is as important as (if not more important than) the actual lockdown.
Just my .02 for what it's worth.