Lain vs. Laid, Passive Voice vs. Participial Adjective
I understand the difference between the verbs lie and lay; however, things seem to become somewhat confusing in certain sentences. For example:
"The books were laid/lain out on the counter." In this sentence, it is possible to read this as a passive-voice construction, in which case laid would be correct. But could you also read this sentence as a non-passive-voice construction, in which case lain would be appropriate, acting as a participial adjective?
Other examples: "The streets were laid/lain out in a square grid." (passive voice = laid; adjective = lain) "The swimmers were lain out on the beach." (adjective = lain)
Lie out, as an intransitive phrasal verb, has two definitions:
1 To rest or recline outside, especially so as to sunbathe.
I'm going to lie out for a while to work on my tan.
I think the girls are all lying out by the pool.2 To be left exposed in or atop something or some place.
You can't leave your tools lying out on the kitchen table like that, Bob—one of the kids could have gotten into them!
I wouldn't let sensitive information like that just lay out in the open for anyone to see, Dan.Source: The Free Dictionary: lie out
Your "swimmer" sentence works with the first definition (I have substituted the present tense for the past and added some adverbs here, to make it easier to see):
Intransitive present perfect: The swimmers have just lain out on the beach.
Linking / participle adjective: Now the swimmers are lain out on the beach. (swimmers = lain out)
That is "correct" but not idiomatic. We would normally say:
Intransitive present progressive: Now the swimmers are lying out on the beach.
Your "book" sentence works with the second definition:
Intransitive present perfect: The books have lain out on the counter since last week.
Linking / participle adjective: Currently, the books are lain out on the counter. (books = lain out)
Similarly:
Intransitive present perfect: The tools have lain out in the rain since Sunday.
Linking / participle adjective: Currently, the tools are lain out in the rain. (tools = lain out)
Again, those are "correct" but not idiomatic. We would normally say:
Intransitive present perfect progressive: The books have been lying out on the counter since last week. The tools have been lying out in the rain since Sunday.
Intransitive present progressive: Currently, the books are lying out on the counter. Currently, the tools are lying out in the rain.
Your "street" sentence does not work with either definition. Let's apply the first definition:
Intransitive present perfect: *The streets have just lain out in a square grid. (incorrect)
Linking / participle adjective: *Now the streets are lain out in a square grid. (incorrect)
Without invoking an extreme case of anthropomorphism, streets (and books) can't lie themselves out like swimmers can; they need an agent—even if unexpressed (as in the passive voice)—to end up in a square grid. And that means only laid out is possible as an adjective here:
Transitive active present perfect: Planners have just laid out the streets in a square grid.
Transitive passive present perfect: The streets have just been laid out in a square grid [by planners].
Linking / participle adjective: Now the streets are laid out in a square grid. (streets = laid out)
Let's apply the second definition:
Intransitive present perfect: *The streets have lain out in a square grid [in the cold night, on the ground] since 1880. (incorrect)
Linking / participle adjective: *Currently, the streets are lain out in a square grid [in the cold night, on the ground]. (incorrect)
No semantic sense can be made of those.
There's a lot more to explore about objectless reflexive verbs (like lie out at defintion 1) and the so-called middle voice (where inanimate objects do achieve a sort of agency: The egg cooked [itself]), but that is for another question.
Intransitive verbs like lie, sit and stand usually function in a similar manner:
The books are lying on the counter.
The books are sitting on the counter.
The books are standing on the counter.
With lie, it is not so easy to determine what the ordinary present perfect* looks like, because it is seldom used. But it is easier with intransitive stand:
The books have stood there for ages.
The books were stood there for ages.
In modern English, I believe you will normally see have/had stood, not were/are stood. The latter is, in my opinion, good English, but it is somewhat old fashioned or formal, as in an epic tale.
This brings us to the books were lain: this is even rarer than were stood, praesumably because the passive construction were laid has pushed it into oblivion. (There is no analogous construction with stand other than that with the transitive verb stand, which is identical in form to the construction with intranstitive stand.) So the verb were in your example strongly suggests it must be laid. The normal way to make a past out of lie is the books have lain.
Then there is evidence from literary usage. Perhaps the most famous example is from Purcell's Dideo and Aeneas:
When I am laid, am laid in earth, May my wrongs create
No trouble, no trouble in thy breast;
Remember me, remember me, but ah! forget my fate.
Remember me, but ah! forget my fate.
Even in this rather formal and old-fashioned usage, laid is used. I believe you will find this throughout (modern) English and not were/are lain, even though the latter is not wrong.
*) Is the were were lain even a present perfect? I'm not sure what the right term is.