public toilet vs lav

public toilet and lav both are nouns.

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

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

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

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