If you wish to move a horse (any horse) from the lateral to the diagonal under saddle all you need to is collect them into an effective bascule
. If you do this the horse will have no choice but to trot. Getting them into a bascule
might be challenging (to the point of serious resistance by the horse). Again, a good rider should be able to accomplish this in a few training sessions. But before they do it they should have a plan and part of that plan is a good reason for the plan!!!
If you don't believe me talk with any dressage trainer. They know all about this (including going from classical collection all the way to rollkur).
I do NOT recommend this for routine work, but for corrective or specialized work it can be an effective tool for addressing some problems.