Lie and lay are words that trip people up. It is because they are really two different verbs. It is the old confusion of transitive and intransitive verbs.
You (present tense) lie down, and yesterday (past tense) you lay down. That is an intransitive verb - no object to the sentence.
You (present tense) lay a table, lay an egg, lay down rules - a transitive verb with an object to the sentence, the thing that you lay. The past tense of THAT lay is laid - "the chicken laid an egg"
You can lay an egg or a table, you can lay a pretty girl, you can lay down your arms or your life, but when you lie down you do it without an object.
It doesn't help that the past of "lie is "lay"
"Mother always lays the table before she lies down for a nap"
"Santa laid his gifts by the fireplace as the children lay sleeping."