Although lie (See lay) is always an intransitive verb (that is, cannot take a direct object), it becomes transitive when preceded by over- or under-. When lie is combined with these prefixes, underlie and overlie in some instances are interchangeable with underlay and overlay: "The principle that underlies (or overlies) his actions is the so-called golden rule." The best rule to follow in choosing which of these four terms to use is to move over or under to the position of a preposition: "The principle that lies (not lays) under his actions...." "The paint that lay over the surface of the wall...." In geology, however, the form lie is preferred: "The clay that underlies the rocky surface...."
Dictionary of problem words and expressions. Harry Shaw. 1975.