'lie' is present tense 'lay' is past tense so in this context 'lay' is incorrect
I'm gonna go "lay" down, that sounds present tense to me, I'm gonna go "lie" down does also
lay is a transitive verb meaning put or place eg Lay the book on the desk.
lay, laid, laid
lie is intransitive meaning recline or situate eg. I'm going to lie down.
lie, lay, lain
According to Macmillan English Dictionary 5 [intransitive] spoken a way of saying ‘lie’, meaning to have your body in a flat position, that many people think is incorrect
It would be wrong if by using that sentence we intend saying "sit down" (instead of lay down)