My trainer has been teaching me and my horse to canter on the correct leads and things lately. (My TWH is just now learning how to canter on cue; she wasn't trained to canter before.) I have learned quite a few handy ways to set her up to successfully strike off in the correct lead. I'll see if I can explain it to you a little bit.
1. It helps big time to practice this on the ground first.
2. Remember to give the horse her face. She will keep thinking she's done the wrong thing if there is never a release.
3. It also helps very, very much if your horse knows how to two-track, and you know how to cue for it.
4. I don't know exactly how you're asking for the canter, but try to cue it from a collected walk, not a trot. And make sure you have specific cues you only use for asking for the canter, not anything else. (i.e. Don't just kick harder to go into a lope.)
5. You can walk in a somewhat small circle and cue the horse to lope before you finish the circle.
6. Or you can walk a half circle, turn back into it like you going to walk a half moon shape, but then yield into the half circle you just made, then before you reach the outside edge of your circle ask for the canter to the inside.
7. Or you can walk along the rail, ask for a rollback, and then cue right out of the rollback into a canter. (It's easier if you're in a roundpen and ask for a rollback to the outside.)
8. Or you can set up some poles in a T shape--so you would be riding in between two poles the whole time--and ask for a lope right before you get to the end of the stem of the T. Turn either to the right or left out of the T. (Geez, I hope that made sense!)
9. Instead of constantly kicking to keep her in a lope, you could try giving a verbal cue along with a nudge with your boot every three strides or so. Keep it controlled and coordinated as best you can.
So, there's a few different things to try out, and there are many more, but I hope this will help you!
**I must not forget to thank the difficult horses, who made my life miserable, but who were better teachers than the well-behaved school horses who raised no problems.**