bathroom vs lavatory

bathroom and lavatory both are nouns.

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

As nouns, bathroom and lavatory are synonyms defined as:

bathroom and lavatory: a room or building equipped with one or more toilets

Other synonyms of bathroom include can, john, lav, privy, toilet.

bathroom (noun)	lavatory (noun)
a room (as in a residence) containing a bathtub or shower and usually a washbasin and toilet	a room or building equipped with one or more toilets
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