To Lie (verb):
1. To tell an untruth : Don't lie to me. You didn't watch the Super Bowl, did you?
past tense: lied : Okay, I lied. I didn't even watch the commercials.
past perfect tense: had lied : If I hadn't lied, you would have made me watch the highlights on the DVR.
2. To repose in a prone position : If football gives you a headache, why don't you go lie down?
past tense: lay : I lay down for an hour, but it didn't help.
past perfect tense: had lain : She had lain in her room for about an hour before her husband noticed that she wasn't present during the halftime show.
To Lay (transitive verb):
To set an object down: Lay down your book and watch the damned game, why don't you?
past tense: laid : I laid down my book for ten minutes, but the game gave me a headache, so I picked up the book again.
past perfect tense: had laid : If I had laid my book down sooner, I wouldn't have missed that touchdown. Oh well. Big whup.
So yes, I admit, too many of these words sound the same, and the tenses get all mixed up in each other's business. Just memorize a few key phrases that are correct and you'll remember the rule for this verb:
Lay down your weapon!
I must go lie down now, even though I lay down ten minutes ago.
Just remember: You can never "go lay down." Lay down ... what? Lay needs a direct object. You have to lay down a book, a magazine, your gun--something. It means put down, or set down.
And you can never "lie down a book." (Not as many people make this mistake.) Lie down is an intransitive verb; it can't take an object. Just lie down your own damned self and be done with it.
image: Madame Recamier by Jacques-Louis David. wikimedia.org