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.