It's complicated. Lie is one tense of the word when referring to yourself.

I want to lie down is correct, and can be remembered by thinking of the word "recLINE" which rhymes. But lay is also past tense of lie.

There are three tenses of verbs in english. Lie lay lain. Then lay laid laid.

Lay is used for placing something like a book or even a baby down.

(BTW, I cheated and asked my mother who minored in English at University. )