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this is a good intro piece to the issue
https://www.macmillandictionaryblog.com/laying-down-the-lie-of-the-land
the conflation has been around for 700 years, apparently.
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Well, I don't agree with the usual 'people have got it wrong for so long that it must now be right' or 'it wasn't considered a mistake back then, so when people consider it a mistake nowadays they don't know the history'. The words quite simply have different origins, reflected in most Germanic languages, e.g. "liegen" ('to lie') and "legen" ('to lay') in German.
https://www.etymonline.com/word/lay
https://www.etymonline.com/word/lie
What happened is that they began to sound more alike, which is when the confusion crept in, and I have no doubt that at times people didn't pay much attention to it, but while it's a fairly inconsequential example, I generally think that different ideas should have different words, and I therefore think it's still very sensible to maintain the distinction between them. Plus, I rather like the participles of 'to lie' and I don't like monodirectional word takeovers ('to lie' isn't used in place of 'to lay'). :)
Erm, this is grammatically correct, and the verb used is 'to lie'. The sentence is a second conditional, which calls for the use of the indicative past ('lay') in the subordinate ('if') clause and the conditional in the main clause.
I agree with you that the conflation of 'lie' and 'lay', especially in American English, is regrettable, but this is not an example of it.