I have seen in English language texts a reference to "lay Jains" or "lay Hindus" who are not monks, nuns, priests, or ascetics, but who live as 'regular people.' Is there a typical way to express this in Hindi (or Sanskrit)?
There is and cannot be any thing like "lay Hindus": what terrible understanding of Hindu thought! "Lay Jains" could mean those who have not taken "deekshaa" yet, but are not living householders' lives and have already started on the path of being a monk: so I don't think it's about being settled, etc. If it were to be about settled, though, then marrish's suggestion works like a charm.
Jains use the word shraavak for lay adherents to the Jina's teachings. There is also upaasak, as in the upaasakadashaH, the 7th of the 12 angas (fundamental Jain scriptures) covering the conduct of a layman. Upaasaka is also the standard word for a Buddhist layman.
And although Christian concepts of laity and clergy obviously don't apply in Hinduism, gRhastha does refer to people who in dharmashaastra are expected to be sexually active, gain wealth to support a family, and perform the shrauta and gRhya sacrifices. This is clearly what the OP is referring to as a "lay Hindu", in contradistinction to a saMnyaasii, who does none of those things.