I think of a horse as having 4 doors, each side and front and back. If you want sideways movement to the left you have to open the left door and close the other 3... Left leg off, left rein open, front and back door closed by controlling forward/backward movement with body and hand, right leg on to ask for the movement but the most important thing is the reward, you absolutely must release the ask the moment he even shifts his weight the right way, gradually you begin to delay this reward, so a weight shift, becomes a step, 3 steps etc if you miss the Try and don't give a reward (that's what tells him the right answer is) for it he will quickly get bored to trying and just do what ever he thinks might be right