'lying down' a horse is something totally different. It consists of pulling a horse's head around until the pressure triggers what is thought to be an 'endorphin release' and the horse can be toppled over. It's very similar to what happens when predators bring a zebra down in the wild.
It should never be used by anyone other that a professional, only in dire situations to help with very dangerous vices and even then only with caution as a last resort, as it doesn't really address the horse's problem. Problem is it's becoming a fashionable natural horsemanship technique now and everyone and their mother is trying it, rarely to the benefit of anyone.
'Trick' lying down is cute. A different thing entirely.