Do you know the difference between “lay” and “lie”?
“Lay” always needs an object. In other words, what is being set down is not the subject of the sentence. I lie down (correct – the subject is reclining); I lay the book/the baby/the remote down (correct – the object is being set down).
Ergo:
Bob Dylan’s “Lay, Lady, Lay…” (no object) should be “Lie, Lady, Lie/ lie across my big brass bed…”
Snow Patrol’s chorus “If I just lay here/if I just lay here…” (no object) should be “If I just lie here.”
Sophie B. Hawkins’s “As I Lay Me Down to Sleep” (object: me) is correct.
Bon Jovi’s “Lay Your Hands On Me” (object: your hands) is correct.