deficit vs lack

deficit and lack both are nouns.

Word	Noun	Adjective	Verb	Adverb
deficit	Yes	No	No	No
lack	Yes	No	Yes	No

As nouns, lack is a hypernym of deficit; that is, lack is a word with a broader meaning than deficit:

Other hypernyms of deficit include deficiency, want.

deficit (noun)	lack (noun)
the property of being an amount by which something is less than expected or required	the state of needing something that is absent or unavailable
an excess of liabilities over assets (usually over a certain period)
(sports) the score by which a team or individual is losing
a deficiency or failure in neurological or mental functioning

deficit (verb)	lack (verb)
	be without
	To be insufficiently prepared