Another great way to train a behavior with Positive Reinforcement is straight up Capturing. This means you just wait for the horse to do the thing you want, then reinforce it heavily! Doing this can allow you to get huge behaviors on cue without much fuss.
The thing is, we don't always just have to sit and wait. Knowing our horse, as an individual, will help us alot with this. When does your horse normally do the behavior you like? Use this information to be ready with your bridge signal and treats right when they do it!
There are some behaviors i will only teach through capturing, so i know they are happening with free choice and no coersion or force or social pressure. Lying down is one of them. I find most horses lie down when they roll after getting wet, after having their blanket taken off, when the soft, sandy footing is just right, or during specific sunny times of the day. Knowing this we can be ready to capture this behavior when our horse feels safe offering this in front of us.