I agree with some of the earlier posts. I think it's highly regional. Almost any non-lawyer, anywhere in the country, is going to have a high initial perception of a HYS grad. After that, there probably aren't many who know the difference between, say, Virginia and IU, or Michigan and Florida. I'm sure there are a lot of non-lawyers who would probably assume that schools with a high academic profile generally (Notre Dame, Duke, NYU, Berkeley), also have respected law schools. You probably wouldn't have a great deal of recognition for otherwise great LS like WashSTL or W&M aside from non-lawyers in those regions.
Another interesting point if you are considering "laypersons" to be non-college graduates: If you are outside of biglaw (especially in flyover country) and the client base is blue collar small business, you'll likely find that even HYS would be trumped by the state school, or if more than one, the more highly respected state school. Sure, it's a stereotype, but people in these areas honestly do look at people coming from those schools with a little bit of suspicion AND there is a very noticeable "ours is as good as yours" type of mentality. Whether or not this overrides their self-interest in hiring the attorney/firm with the best law school credentials would be a good question - but my guess is that it happens more often than not. But I suppose that goes less to perception and more to personal client preferences - so it doesn't really address the OP topic. But it's worth thinking about, I suppose.
Interesting topic, OP.