lack vs deficit

lack and deficit both are nouns.

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

As nouns, deficit is a hyponym of lack; that is, deficit is a word with a more specific, narrower meaning than lack:

Other hyponyms of lack include absence, dearth, famine, shortage, mineral deficiency, shortness, stringency, tightness.

lack (noun)	deficit (noun)
the state of needing something that is absent or unavailable	the property of being an amount by which something is less than expected or required
	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

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