layman vs lay reader

layman and lay reader both are nouns.

Word	Noun	Adjective	Verb	Adverb
layman	Yes	No	No	No
lay reader	Yes	No	No	No

As nouns, lay reader is a hyponym of layman; that is, lay reader is a word with a more specific, narrower meaning than layman:

layman: someone who is not a clergyman or a professional person
lay reader: a layman who is authorized by the bishop to read parts of the service in an Anglican or Episcopal church

layman (noun)	lay reader (noun)
someone who is not a clergyman or a professional person	a layman who is authorized by the bishop to read parts of the service in an Anglican or Episcopal church