Laying down is the -ing form of 'lay down,' meaning to place or set something on a surface. It can also mean to set rules or surrender, as in 'laying down arms,' not 'lying down' to recline.
Or certainly I would need time - which I would love to have but there almost never is on a film - to just spend a week with a roomful of guys laying down these patterns. Danny Elfman
The phenomenological world is not the bringing to explicit expression of a pre-existing being, but the laying down of being. Philosophy is not the reflection of a pre-existing truth, but, like art, the act of bringing truth into being. Maurice Merleau-Ponty
By laying down the relativity postulate from the outset, sufficient means have been created for deducing henceforth the complete series of Laws of Mechanics from the principle of conservation of energy (and statements concerning the form of the energy) alone. Hermann Minkowski
Yes, she thought, laying down her brush in extreme fatigues, I have had my vision. Virginia Woolf
The best opinion now is, that there are multitudinous forms which are not sufficiently differentiated to be distinctively either plant or animal, while, as respects ordinary plants and animals, the difficulty of laying down a definition has become far greater than ever before. Asa Gray
If you spit laying down it will only come back in your mouth. Amharic Proverb