the "lift, shift, change" is great. never heard it called that but have always done a 3 part signal. the horse then is prepared for the change, and gathered and ready. time it with his stride and be sure to ask at the right part of the stride. the "lift" will gather him a bit, the shift will warn him what's coming, then he is ready for the change signal.
also a great teaching cheat is to do this in a place where the change puts them heading where they want to go. when you are first teaching this. later when they know it, it will work elsewhere.