By noon, the cat had ___ in the patch of sunlight for three hours.
Explication
The cat had been reclining, so the past participle lain follows had. Laid would imply that the cat placed an object, which the sentence neither names nor means.
The cat had been reclining, so the past participle lain follows had. Laid would imply that the cat placed an object, which the sentence neither names nor means.