Ask for the next gait before your horse reaches the lunging flags. An October demo player reported that the horse needs to be moving in the requested gait as it passes them. That gives you a practical cue to test in your current version.
Read the next flag
Look ahead to the upcoming gait cue instead of waiting for the horse to reach the flag. Think about the gait you need at the marker and allow the horse time to settle into it.
Test one transition at a time
If you keep getting the flag wrong, ask a little earlier on the next pass. Use the game's feedback to see whether the horse reached the requested gait in time. Keep the rest of the approach similar so you can tell what changed.
Use a separate cue for Caprilli
Community reports describe the Caprilli transition at the boundary between gait sections. In lunging, use the flag to check the gait you have already established. See the Steam discussion on lunging and gait transitions for the original October player observations.
FAQ
Do I change gait at the flag?
Try changing before it so your horse is already in the requested gait when it passes.
Is there a fixed number of seconds to wait?
The player report gives a visual cue. Use the training feedback to calibrate the timing in your build.
Does this work the same way in Caprilli?
October players described a different cue for Caprilli. Follow the boundary between the gait sections there.