Brooke - I remember us discussing this before as well, but I have no idea where or when. So maybe both of us are losing it! However, I agree that the change is fairly insignificant. I think the change that Soda mentioned in the LITFL lyrics though changes the meaning of the line a lot.
FP - in the U.S., we commonly use lay the same way that it is used in the song, so it seems very natural here. Don't want to get into an English grammar lesson but in common everyday use here, we generally differentiate between them by using lay as a transitive verb and lie as an intransitive verb. We use the word 'laid' as the past tense.