desire vs lust

desire and lust both are nouns.

Word	Noun	Adjective	Verb	Adverb
desire	Yes	No	Yes	No
lust	Yes	No	Yes	No

As verbs, lust is a hyponym of desire; that is, lust is a word with a more specific, narrower meaning than desire:

desire (noun)	lust (noun)
an inclination to want things	self-indulgent sexual desire (personified as one of the deadly sins)
the feeling that accompanies an unsatisfied state	a strong sexual desire
something that is desired

desire (verb)	lust (verb)
feel or have a desire for; want strongly	have a craving, appetite, or great desire for
express a desire for
expect and wish