In short 'lay' = 'to put something down'. If something is lying by itself you use 'lie'.
I'm a native English speaker and its "lying" not "laying". As #tadjanow says, "lay" is what you do to something (or someone!) else.
There is a usage "lay yourself down" but it needs the reflexive pronoun (or whatever its called in English, don't ask me! lol), and its the action of going INTO that position, not being in that position.
Colloquially in some parts of the English speaking world you can use lay = lie (cf. Bob Dylan, "Lay Lady Lay") but its not middle English.
At school our textbook used the term middle English to describe a form of standard English that could be used and understood anywhere throughout the modern English-speaking world.
This is totally different from the term Middle English (captial "M").
I did a google search for "middle English" and couln't find any instances of the old meaning I was taught. Maybe it's a term that is fallen out of use? Anyway, I will stop using it because it's so easily confused with "Middle English".
Maybe a better term for me to express the concept I wanted to express above is: "Standard written English".