The reason is that the verb "lie" in this context means "to recline" and is an irregular verb. Its past tense and past participle are "lay" and "lain".
Here's a breakdown:
* Present Tense: He prefers to lie down.
* Past Tense: He preferred to lie down.
* Present Perfect: He has preferred to lie down.
* Past Perfect: He had preferred to lie down.
It's easy to confuse "lie" with "lay," which is a different verb meaning "to place" or "to put something down."