Someone needs to lay down the law about the use of "lie" vs. "lay." But therein lies the rub: folks never learn the principal parts of verbs in school anymore (though in my own case, I picked up the right usage of verbs simply from reading and from parents who were grammar sticklers; I never encountered a "principle part" till I started Latin my junior year of high school). So, for quick reference:
Lie, lay, lain (intransitive, i.e. it can not take an object)
lay, laid, laid (transitive, i.e. MUST, MUST, MUST take an object!!!!)
(I suppose a Marxist instructor might resort to scurrilous examples here to enhance pupils' attention, but I will refrain---if only because I scorn Marxist pedagogy, having been subject to way too much of it myself, viz. "There IZZZZZ no such thing as 'correct grammar'!" A not surprising attitude: once you chuck absolutes in morals and ethics, then tossing out grammar is a footnote.)
So, here are some examples:
1. I usually don't lie in the sun, but yesterday, I lay there for a few minutes in a vain attempt to bronze a bit. I have never lain in the sun for hours and hours---I lay great stress [this is the object] on not looking like Geronimo in old age...even if wrinkles supposedly make guys look more distinguished. (And no, I do not "lay me down to sleep" in the sun, either. [Notice that "me" there functions as the object, so it's grammatically fine, even if stylistically archaic.])
2. Lay down your weapons [object], fiend!
3. Lie down, Fido!
4. Where are my keys? I laid them [object] down on the table a few minutes ago! I'm in the habit of laying them down there, after all. But now they're not lying there anymore, darn it!
5. That rusty old wagon wheel has lain/been lying around here since my grandpa's time.
6. Marxists have never laid much stress [object] on grammar. They lay [present tense] more emphasis [object] on "getting laid." It will be a day for rejoicing when they all lie in their graves, every last one of them. (Hopefully soon, since for decades they've pushed contraception and foetus slaughter---no doubt a logical agenda when your whole life revolves around getting "laid".)
NOTE: Do not confuse the 2 uses of "lay": simple past tense of "lie" vs. present tense meaning "to put down" (transitive). Same word, different functions.