I agree with Mls too. She probably isn't comfortable and/or doesn't have the appropriate muscling to canter/lope easily, so she's rushing. I wouldn't be working on loping anyways until you can get her to trot slowly w/ impulsion/power. That's a good way to help her build the necessary muscle. It'll help your riding ability too.
What *I* do (disclaimer - I am not a "trainer") is work on get a forward balanced trot. I do circles and serpentines and work on bending/flexibility. Then I work on slowing the trot by slowing my posting, then I speed it up again, then slow down, etc. I work large circles and shallow serpentines at first and gradually shrink the circles and tighten the serpentines as the horse shows it's capable and comfortable doing what I ask. After all that's said and done I move to canter work and use the same progression. Let the horse get balanced and forward, then work on bending/flexibility, and then work on transitioning between speeds within the gait.
My goal is to keep the horse relaxed, responsive, and forward moving with impulsion. I don't want a foot dragging lazy canter or trot, but I do want them to slow it down and keep the power. If that makes sense. One thing I do not (or try not) to do is mess with their head/mouth in terms of pulling them to slow down. I don't want them bracing against the bit and falling onto their forehand.
Again, I am NOT a trainer, but this is what I've been doing and it seems to be working well. I'm sure it would go better for me if I had a trainer and THAT is what I would recommend to you.
Anyone else with more experience feel free to correct me