I've read SOME of the posts here, but not all, so bare with me:)
I agree with some....
If a horse knows how and can physically pick up the correct lead, then it's a matter of telling him what you want, not a matter of how far you let or make him lope after he picks up the correct lead.
My horse has a stiff side, but he knows what lead departures are all about. Initially picking up the correct lead was troublesome for me, not him!
This is what I do:
I begin by working on getting him really soft and light sided. Move off myers and my hands, the more I ask, the more you move - softly.
I walk collected circles, trot collected circles, all soft and at the speed I want. While trotting or walking collected circles I push his hip to the inside. When I am satisfied he is moving of my legs nicely and softly, I keep my outside leg on and that inside hip in, place my inside leg on his girth and kiss to him, all while increasing my leg pressure (this happens in a matter of seconds) on until he picks up the lead I'm asking for.....then I release and let him lope relaxed, for however long I choose.
Now, if he doesn't move that hip over and lope when I ask, I very abruptly bring him down, turn his nose to the outside and get after him to move his hip over and turn him in tight circles.....essentially I am making it harder for him not to pick up the correct lead and then I try again....his release is to lope off on the correct lead, whatever happens after the departure is just another aspect of the lope.....I like to break things down like that.
The lope is more than just the lead departure....it's very easy to get caught up in the lope as a whole....breaking it down into parts makes it much easier to work on:)