closet vs lav

closet and lav both are nouns.

Word	Noun	Adjective	Verb	Adverb
closet	Yes	No	Yes	No
lav	Yes	No	No	No

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

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

closet (noun)	lav (noun)
a small private room for study or prayer	a room or building equipped with one or more toilets
a toilet in Britain
a tall piece of furniture that provides storage space for clothes; has a door and rails or hooks for hanging clothes
a small room (or recess) or cabinet used for storage space

closet (verb)	lav (verb)
confine to a small space, as for intensive work