lumber vs cut down

lumber is a noun but cut down is not a noun.

Word	Noun	Adjective	Verb	Adverb
lumber	Yes	No	Yes	No
cut down	No	No	Yes	No

As verbs, cut down is a hypernym of lumber; that is, cut down is a word with a broader meaning than lumber:

Other hypernyms of lumber include drop, fell, strike down.

lumber (noun)	cut down (noun)
an implement used in baseball by the batter
the wood of trees cut and prepared for use as building material

lumber (verb)	cut down (verb)
cut lumber, as in woods and forests	cut down on; make a reduction in
move heavily or clumsily	intercept (a player)
	cause to come or go down
	cut with a blade or mower
	cause to fall by or as if by delivering a blow
	cut with sweeping strokes; as with an ax or machete