lie vs lie down

lie is a noun but lie down is not a noun.

Word	Noun	Adjective	Verb	Adverb
lie	Yes	No	Yes	No
lie down	No	No	Yes	No

As verbs, lie and lie down are synonyms defined as:

lie (noun)	lie down (noun)
a statement that deviates from or perverts the truth
position or manner in which something is situated

lie (verb)	lie down (verb)
tell an untruth; pretend with intent to deceive	assume a reclining position
be lying, be prostrate; be in a horizontal position
assume a reclining position
be located or situated somewhere; occupy a certain position
originate (in)
have a place in relation to something else
be and remain in a particular state or condition