The word layperson meant, originally, a non-ordained member of the church. Well, actually maybe it didn't since it's apparently pretty a recent (1970s) version of layman, but you know what I mean. It also means, in a more general sense, not a member of a specialist community or not having specialist subject knowledge. So I might use it when I'm talking to students like this:
Linguists tend to have different judgements than laypeople do.
And then I mean, of course, non-linguists. It's a term that gets its meaning from being in opposition to something else. If I said Laypeople find this sentence ambiguous, you might infer that I meant non-linguists because I'm talking about linguists, but you might not. And if I was just out and about and I said What do laypeople have for breakfast?, the most plausible interpretation would probably have to be the 'not a member of the clergy' one. Which would be weird, but it's the only meaning of the word that is sort of independent of context.
I was thinking about this because I always use it kind of jokingly in this way, in much the same way as I refer to non-linguists as 'normal people', but I was reading a recent paper by Lelia Glass where she uses it totally non-ironically (as far as I can tell, anyway) to refer to people who aren't strength-training enthusiasts. I'd thought the more generalised 'non-specialist' meaning was fairly recent and not as well-established as the 'non-clergy' one, but a check on Etymonline tells me that I'm wrong, and both are pretty much as old as each other. While lay does come from a French word meaning 'secular', ever since we've used it in English, more or less, it's had the general meaning of 'non-expert' too.