Indeed, lay(past= laid) requires a direct object and lie(past lay) does not. No one put there but you put YOURSELF. (no direct object) Howeve, you laid something or someone onto something means that this person or thing didn't put itself down but someone did.
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TerryxpressHence,Next to the girl lay (Past Tense of 'to lie') a cushion...The cushion was there, lying on the floor. It was "in a resting position on a supporting surface".I'm afraid I don't agree with you Terry.Did you ask who put down the cushion ?,it's true,it's there but not by itself .