lack vs shortness

lack and shortness both are nouns.

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

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

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

lack (noun)	shortness (noun)
the state of needing something that is absent or unavailable	an abrupt discourteous manner
	the property of being shorter than average stature
	the property of being of short temporal extent
	the property of being of short spatial extent
	the property of being truncated or short
	the condition of being short of something

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