public convenience vs lav

public convenience and lav both are nouns.

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

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

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

public convenience (noun)	lav (noun)
a toilet that is available to the public	a room or building equipped with one or more toilets