public lavatory vs public convenience

public lavatory and public convenience both are nouns.

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

As nouns, public lavatory and public convenience are synonyms defined as:

public lavatory and public convenience: a toilet that is available to the public

Other synonyms of public lavatory include comfort station, convenience, public toilet, restroom, toilet facility, wash room.

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