The left hand prevents the horse from getting away to the front and by opposing the forehand to the haunches, assists the action of the whip in moving the hind quarters.
In this movement the forehand should move and the fore legs should cross, but on an arc of very small radius.
Dismounted work should be considered as of only secondary importance. It will be of great benefit with some horses and practically useless with others. In any case, dismounted lessons should always be very brief.