The verb here is 'to lay' : to place SOMETHING gently in a horizontal position.
So, we have the declension of that infinitive, where the Past Tense, and Past Participle are 'laid'.
'to lie' means 'to be at rest in a horizontal position'.
A mother lays a baby in a cot. The baby is now lying in the cot (NOT 'laying').
The boy lays his pencil on the desk. The pencil now lies on the desk.
Some bricklayer laid the brick in its place. The brick has now lain there for 20 years.