Lay is a transitive verb and needs an object - lay (something)
down or lay down (something) Lie is intransitive and doesn't need
an object - i lie on the floor
The confusion arises from the fact that "lay" is also the past
tense of "lie"
In the present "I lie in my bed" In the past "I lay in my
bed"
I would recommend "Lie down and go to sleep.".
But now I lay me down to sleep. Because the object is me (though
it should be myself).