While its not a trick I would teach a riding horse or a large horse because of the stress on joints. I also don't really see the point of it; however, that's just me.
I have heard of folks clicker training a horse and then hosing the horse off and clicking when they went down to roll. I don't know if this would teach them to roll or lie down. I would investigate that method because then the horse in theory controls how they lie down (speed and body position) and when they go down. The other option would be to clicker train and then when you find the horse lying down you click and treat that.
I would ask how big this companion horse is? The size could influence how you teach the trick if you use a conventional lying the horse down method. Which can be very stressful for some horses. If you teach them do lie down as a reaction to pressure I can see how a horse would lie down when you got on them. I heard of a horse that was taught to give to pressure so well that when the person got on for the first time the horse lied down.
Again, its not something I would do. I think there are better/more interesting tricks out there. Something like a freestyle dancing with the horse could be interesting.