Lie and lay would not be confusing at all if not for the past tense. That’s where it all goes bad.
Lie, remember, takes no object. Chickens do not lie an egg!
Past tense of lie: lay. Past perfect tense (the one that goes with have): lain.
Like this: I lie down today. I lay down yesterday. I have lain down many times.
Lay takes an object. You cannot simply lay; you must lay something. A chicken lays an egg.
Past tense of lay: laid. Past perfect tense: laid.
The chicken lays an egg today. The chicken laid an egg yesterday. The chicken has laid many eggs.
For extra credit: if you are lying, as in telling fibs, none of this applies. You lie today, you lied yesterday, you have lied often. Shape up and start being more honest.
For extreme extra credit: why does the children’s prayer say, “Now I lay me down to sleep?” I’m not a chicken; why am I laying?
Lay is correct in this case (a bit archaic) because it takes an object: me. The speaker is laying something (themselves) down to sleep. Please do not use this as a model in your head when you are trying pick between lie and lay. It’ll just confuse you. Stick to the chickens.