Laying me out to lie there, but not lying about it

A friend of mine who learned English as a second language, just hit me with a stumper over lunch. What is the exact rule for using "lie" or "lay", in a sentence where someone or something is lying down or laying?

I knew what sounded right to my ear, both formally and in typical conversation; but I couldn't formalize the rule.

So, obsessed, after drawing a full grid, and then throwing up my hands and researching it on the web, it appears the lie vs. lay rule is most succinctly:

The word ‘lie’ or variations of it can only be used in the present or future tense, AND only if the speaker is referring to someone or something that is reclining (and not being merely placed somewhere.)

The lie vs. lay confusion is caused by three main, colliding factors:

1. “lie” and “lay” sound similar, but are actually separate and distinct verbs. “Lie” means “to recline”, whereas “lay” means “to place somewhere”.
2. to muddy things further, the past tense of the verb “lie” (to recline) is the word “lay”. So even though this “lay” sounds the same as the verb “lay” (to place somewhere), it really is a different word.
3. further spinning things around, the "past participle" (hypothetical phrasing) of the verb "lie" is "lain", while the past participle of the verb "lay" is "laid".

So “I’m lying down,” “I lie down,” “She is lying down,”, “The cat lies on the table” or “They’re all lying down, and they're going to keep lying down after eating that much turkey” and are all correct.

But if the speaker is referring to him or herself reclining in the past or hypothetically, it's lay or lain. Such as “Then I lay down and slept,” or "I would have lain down if I could".

And if referring to placing something somewhere, it's always lay or laid. Such as "I lay the book on the table", and "I would have laid down the books if I could"

Whew.

Basic rule of thumb:

You LIE down but you LAY something else down, when speaking in the present tense.

Also it may help to remember that you never lay someone down on something. Only something on something. Laying someone is an entirely different verb. An awesome one.

So “The cats lie on the sidewalk,” but “The leaves lay on the sidewalk.” The exception to this rule would be when an object is being treated as alive for poetic effect. (i.e. “The building lies in ruins.” Vs. “The building lays on a concrete foundation.”)

And there we shall let the sleeping grammar dogs lie. Before I get laid off.