Move his shoulder across the diagonal with your inside leg and rein and count for three strides. after he lifts for the fourth stride, take off your inside leg/rein and use your outside leg/ rein. Hope that helps!
Be persistent. Do a circle then really push him the other way and counter bend and keep your leg on until he changes
Horse is either not physically ready to perform it. Or he isn't balanced to do it. Work in his balance and yours. You have to be able to shift your weight with him to perform the action. But if he can't counter canter on command or do lateral work he isn't physically ready as he doesn't have the right muscle groups developed.
I would work first work on just trotting across the ring like your doing a change and practice the bend of your horses head. Slowly move along to cantering then doing a simple change, adding a pole and cantering to the pole and trying to get it over it, and then finally take the pole away and try it. Keep in mind some horses can't do it on the flat it is just to much to process for them like my pony can only get them over jumps because he gets confused so I just stick to simple changes on the flat.
Work on doing figure eights when riding. Try setting up two cones in the middle to pass through. Canter your 20 meter and when coming to the centerline at x trot, ask for other lead and change direction. Continue to do this with as little as possible trot steps in between your change.