The word "lie" is an intransitive verb that means "to be or to stay at rest in a horizontal position." An intransitive verb conveys a doable activity and is not received by a direct object. You can lie on the couch, or on the bed. You cannot lie books on a shelf.
The word "lay" is transitive, meaning that it must be received by a direct object. "Lay" is defined as "to put or set down." Therefore, you may lay books on a shelf, but you cannot "lay" on the couch, or on the bed.
The man was lying on a beach towel in the front yard.
The man was laying a beach towel on the front lawn.
After I laid the books on the shelf, they remained lying there until I took them down again.
I told an untruth while reclining in a hammock. I was guilty of lying while lying.
You don't need to be an English graduate student to learn such simple grammatical distinctions. Yet, learning such distinctions between similar words dramatically increases the effectiveness of your spoken and written communication.