lawlessness vs illegality

lawlessness and illegality both are nouns.

Word	Noun	Adjective	Verb	Adverb
lawlessness	Yes	No	No	No
illegality	Yes	No	No	No

As nouns, illegality is a hypernym of lawlessness; that is, illegality is a word with a broader meaning than lawlessness:

lawlessness: illegality as a consequence of unlawful acts; defiance of the law
illegality: unlawfulness by virtue of violating some legal statute

lawlessness (noun)	illegality (noun)
illegality as a consequence of unlawful acts; defiance of the law	unlawfulness by virtue of violating some legal statute
a state of lawlessness and disorder (usually resulting from a failure of government)