absence vs lack

absence and lack both are nouns.

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

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

Other hypernyms of absence include deficiency, want.

absence (noun)	lack (noun)
failure to be present	the state of needing something that is absent or unavailable
the state of being absent
the occurrence of an abrupt, transient loss or impairment of consciousness (which is not subsequently remembered), sometimes with light twitching, fluttering eyelids, etc.; common in petit mal epilepsy
the time interval during which something or somebody is away

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