shortness vs lack

shortness and lack both are nouns.

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

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

Other hypernyms of shortness include deficiency, want.

shortness (noun)	lack (noun)
an abrupt discourteous manner	the state of needing something that is absent or unavailable
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

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