take lying down vs stand

take lying down is not a noun while stand is a noun.

Word	Noun	Adjective	Verb	Adverb
take lying down	No	No	Yes	No
stand	Yes	No	Yes	No

As verbs, stand is a hypernym of take lying down; that is, stand is a word with a broader meaning than take lying down:

Other hypernyms of take lying down include abide, bear, brook, digest, endure, put up, stick out, stomach, suffer, support, tolerate.

take lying down (noun)	stand (noun)
	a defensive effort
	a stop made by a touring musical or theatrical group to give a performance
	a support or foundation
	tiered seats consisting of a structure (often made of wood) where people can sit to watch an event (game or parade)
	a platform where a (brass) band can play in the open air
	a support for displaying ot holding various articles
	a small table for holding articles of various kinds
	a booth where articles are displayed for sale
	a mental position from which things are viewed
	an interruption of normal activity
	a growth of similar plants (usually trees) in a particular area
	the position where a thing or person stands

take lying down (verb)	stand (verb)
suffer without protest; suffer or endure passively	put up with something or somebody unpleasant
	have or maintain a position or stand on an issue
	withstand the force of something
	be standing; be upright
	put into an upright position
	be available for stud services
	hold one's ground; maintain a position; be steadfast or upright
	be tall; have a height of; copula
	be in effect; be or remain in force
	occupy a place or location, also metaphorically
	be in some specified state or condition
	remain inactive or immobile