Snow Patrol’s hit song “Chasing Cars” is well known:
If I lay here
If I just lay here
Would you lie with me and just forget the world?
Of course, song lyrics often disobey the normal rules of English usage. But technically, “If I lay here” is past tense. The opening lines of this song are actually saying If I was lying here, If I was just lying here. But this isn’t what they mean to say. They mean to say If I lie here.
By the time we get to the question, in the third line of the song — Would you lie with me — they get the present tense right. (Why did they change from lay to lie? Is there a rule that says you switch to lie if you add with? Nope.)
English is a complicated language, especially when it comes to lay and lie and all their various forms.
I lie today — meaning I’m lying down. (You can say, for example: “Leave it where it lies.”)
I lay yesterday — meaning I was lying down. (Leave it where it lay. Meaning: It was fine right where it was.)
But you can also lay something down today — although this is a different word, actually. And if you did it yesterday, you didn’t lie it down; you laid it down.
None of which has anything to do with telling a lie. You lie today, you lied yesterday. If you fibbed in bed, you lied as you lay. It sounds wrong, but it’s right.
Then again, if you’re writing a song, you do whatever sounds right, I guess. La la la!