restroom vs lavatory

restroom and lavatory both are nouns.

Word	Noun	Adjective	Verb	Adverb
restroom	Yes	No	No	No
lavatory	Yes	No	No	No

As nouns, lavatory is a hypernym of restroom; that is, lavatory is a word with a broader meaning than restroom:

Other hypernyms of restroom include facility, bathroom, can, john, lav, privy, toilet.

restroom (noun)	lavatory (noun)
a toilet that is available to the public	a room or building equipped with one or more toilets
	a bathroom sink that is permanently installed and connected to a water supply and drainpipe; where you can wash your hands and face
	a toilet that is cleaned of waste by the flow of water through it