I’m guessing that within ten years the distinctions between these two words will have disappeared. But until September 2026, you might consider sticking to the following rules.
LIE (we’re not going to deal with the situation in which the truth is ignored) means to lie down, to rest or recline. Every day after lunch, I lie down. I don’t lay down. I lay something down.
LAY means to put or place: Every day when I lie down, I lay my head on my pillow.
That covers the present tense of both verbs. It gets a little sticky when you go into past tenses:
LIE in the past tense is (wait for it) LAY. Yesterday after lunch, I lay down. OMG, in the present tense you lie down, but in the past tense you lay down! Remember, I don’t make these rules up; I just teach them.
It gets even worse: in the past perfect tense, when has, had or have is part of your verb, you need LAIN. (I bet you’ve never written that word in your life—but it’s not too late to start.) Every day after lunch, I always have lain down.
As for the past tenses of LAY, here is what you want: Yesterday I laid my head on my pillow. I always have laid my head on my pillow.
If your head is aching, perhaps you’d like to lay your head on your pillow.