A Google search for “lay lie” brings up 482,000,000 hits, most of them links to articles that explain the difference between these two verbs. You’ll find two of my own attempts at enlightenment in the DWT archives (here and here).
One of the most astonishing things about this pair of verbs is how long they have been in common use with more or less the same meaning. The earliest example given for lay in the OED is from a translation by Alfred the Great (849-899). The earliest for lie is from the Homilies of Abbot Aelfric of Eynsham (955-1010).
English speakers have been mixing up transitive lay with intransitive lie for a long time. All school textbooks and style guides printed during the past hundred years or so contain sections explaining the usage, but millions of English speakers continue to say,
Lay down Fido.
The body was laying in the alley.
I laid on the deck for an hour.
The most usual error is to use lay intransitively, but some poor conscientious souls–aware that lay is often the wrong choice–are falling into the error of using lie transitively:
‘You got him,’ said Tinker, lying the piece down. –Unnatural Habits by Kerry Greenwood, a Phryne Fisher Mystery, Poisoned Pen Press, 2012, page 227.
The misuse of lay is not merely an issue that distresses English teachers. Advertisers are aware of it and some of them will go so far as to change their ads when the error is pointed out to them. I’m thinking of a Sleep Number ad in which a salesman in a blue shirt is telling how beds used to be sold. The first several times I saw the ad, the man said that customers were told, “Lay over there.” At some point, the soundtrack was changed. The man now says “Lie over there.” I suspect the agency received a lot of letters on the subject.
For my own part, I’ve become partially inured to the intransitive use of lay. I hardly notice it in the course of daily conversation. The alarm clangs only when I observe its use by teachers, broadcast journalists, advertisers, doctors, lawyers, and anyone else whose occupation requires the use of English for public communication.
I cringe when a medical practitioner tells me to “lay down.” When I’m given printed forms containing the error, I correct them in ink before giving them back.
Noblesse oblige. People who invest 12-20 years getting an education can be expected to master a standard form of their native tongue.
I’m aware that much of today’s standard usage was judged non-standard in previous generations. The verbs lay and lie may eventually become so intertwined that everyone will think of them as the same verb. Until that time comes and everyone has forgotten the distinction, “The body was laying in the alley” is nonstandard English.
Bottomline: Eventually it won’t matter to anyone, but for the present, if you have a professional persona to maintain, you may wish to avoid using lay intransitively when the intended meaning is “recline.”