I also want to teach my horse to lay down, but still haven't gotten there yet. I wouldn't attempt this untill your horse has complete trust and confidence in you. Horses can only go 6 ways, up, down, right, left, forwards, backwards. Can you get your horse to do all of those? If you can then your probably ready to try this, but if not I wouldn't try to push your horses trust or confidence. It will come with time, but do it in the horses time.
Hope this helps! :)
Level 4 parelli student, Kolson
"The wind of heaven is that which blows between a horses ears."