legitimacy vs lawfulness

legitimacy and lawfulness both are nouns.

Word	Noun	Adjective	Verb	Adverb
legitimacy	Yes	No	No	No
lawfulness	Yes	No	No	No

As nouns, lawfulness is a hypernym of legitimacy; that is, lawfulness is a word with a broader meaning than legitimacy:

legitimacy: lawfulness by virtue of being authorized or in accordance with law
lawfulness: the quality of conforming to law

legitimacy (noun)	lawfulness (noun)
lawfulness by virtue of being authorized or in accordance with law	the quality of conforming to law
undisputed credibility