In most cases in medieval sources (although there are a few exceptions) the heraldry on the right side of the horse is reversed so the lion appears looking forward. That's also true whatever the arms are (even if not representing an animal or whatever).
It did not change in modern times apparently
"American flag patch is to be worn, right or left shoulder, so that the star field faces forward".a Lion Rampant facing left on one side
Actually in heraldry terms it's facing "dextre" (the right, from the shield bearer point of view).