To lay means "to put" or "to place" and is used transitively. If you put something down you lay it down. Past tense: "I laid" Past participle: "I have laid."
All this may sound complicated, but it is worth learning, if only to avoid saying that you are about to produce eggs when you claim that you are going to "lay down." When Bob Dylan sings "Lay lady lay / Lay across my big brass bed," he is committing a similar crime.
The other verb "to lie" means "to say something untrue" and its parts are agreeably simple (I lie, I lied, I have lied). The pun "you lie like a rug" is correct in both senses.
Dictionary of Usage
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