“Laying back” and “Lying back” are both correct and mean the same thing with a subtle difference.
“Lying back” describes the position of the person(on your back). “Laying back” describes the position(on your back) but also describes the attitude of the person(They are being lazy).
Lying back means that you are in a horizontal position. We often use “lying back” when someone is more horizontal than “sitting down” but not quite completely horizontal. We use “lying down” when someone is completely horizontal and in bed.
Peter is lying back in his bed(he might be sitting on some pillows).
“Laying back” has the same meaning as “lying back” but adds more meaning.
“Laying back” means that somebody is “lying back” in a lazy manner.
Look at him laying back in his hammock without a care in the world.
What about “laid-back”?
“Laid-back” is an adjective that describes someone who is relaxed and doesn’t get stressed very often.
He is very laid back. He never causes any trouble.
It is important to note that “Laid-back” is a positive adjective so it always has a positive connotation.