He ____ to the police about where he had been that evening.

Explication

Telling an untruth is the regular verb lie — lied — lied, so the past simple is lied. The identically spelled reclining verb runs lie — lay — lain, so lay would say that he stretched out somewhere, and lain is that same reclining verb's participle, which cannot stand alone as a past tense without have or had.