public lavatory vs bathroom

public lavatory and bathroom both are nouns.

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

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

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

public lavatory (noun)	bathroom (noun)
a toilet that is available to the public	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