come up vs lift

come up is not a noun while lift is a noun.

Word	Noun	Adjective	Verb	Adverb
come up	No	No	Yes	No
lift	Yes	No	Yes	No

As verbs, lift is a hypernym of come up; that is, lift is a word with a broader meaning than come up:

Other hypernyms of come up include arise, come up, go up, move up, rise, uprise.

As verbs, come up and lift are synonyms defined as:

Other synonyms of come up include arise, go up, move up, rise, uprise.

come up (noun)	lift (noun)
	the act of raising something
	plastic surgery to remove wrinkles and other signs of aging from your face; an incision is made near the hair line and skin is pulled back and excess tissue is excised
	the act of giving temporary assistance
	a ride in a car
	transportation of people or goods by air (especially when other means of access are unavailable)
	lifting device consisting of a platform or cage that is raised and lowered mechanically in a vertical shaft in order to move people from one floor to another in a building
	a powered conveyance that carries skiers up a hill
	one of the layers forming the heel of a shoe or boot
	a device worn in a shoe or boot to make the wearer look taller or to correct a shortened leg
	the event of something being raised upward
	a wave that lifts the surface of the water or ground
	the component of the aerodynamic forces acting on an airfoil that opposes gravity

come up (verb)	lift (verb)
result or issue	perform cosmetic surgery on someone's face
start running, functioning, or operating	remove from a surface
gather or bring together	put an end to
gather (money or other resources) together over time	remove (hair) by scalping
bring forth, usually something desirable	rise upward, as from pressure or moisture
come up, of celestial bodies	invigorate or heighten
come to the surface	raise in rank or condition
move toward, travel toward something or somebody or approach something or somebody	remove from a seedbed or from a nursery
move upward	take off or away by decreasing
get something or somebody for a specific purpose	cancel officially
originate or come into being	call to stop the hunt or to retire, as of hunting dogs
be mentioned	make audible
	take hold of something and move it to a different location
	raise or haul up with or as if with mechanical help
	take (root crops) out of the ground
	fly people or goods to or from places not accessible by other means
	raise from a lower to a higher position
	move upwards
	move upward
	make off with belongings of others
	take without referencing from someone else's writing or speech; of intellectual property
	pay off (a mortgage)
	take illegally
	rise up