My mare did this on a continual basis... She was "left hooved" so to speak. So every time we loped/cantered she'd pick up her left lead even when I wanted her right lead.
I had someone watch us, and they pointed out what I had thought... because its a preferance, she drops her right shoulder and simply cannot pick up her right lead.
To fix this, I picked up her right shoulder, and also made her run slightly crooked (I cant think of the proper word right now
) so that her right hind hoof would be in a better position to begin leading when I asked for her to lope. Also, making sure you are asking for the lead while turning rather than running a straight away will make it easier for her.
Have him collect her some, wait till he is beginning to bend into a right turn (like at the end of the arena), and touch behind the girth to move her hip away (thats how I cue anyways) and ask for the canter, all while raising her right shoulder.
See if that helps and let us know how it goes