toilet facility vs lavatory

toilet facility and lavatory both are nouns.

Word	Noun	Adjective	Verb	Adverb
toilet facility	Yes	No	No	No
lavatory	Yes	No	No	No

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

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

toilet facility (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