This statement may at first sound like doubletalk but is indeed logical. If nothing has meaning, then we could never discover its meaninglessness. To recognize something as having no meaning necessitates the understanding of "meaning" itself.
Lewis may have existentialist philosophy in mind here. Existentialism was a reaction against belief in natural law and Hegelian philosophy. Considered an outdated movement now, it is defined as "a philosophy that emphasizes the uniqueness and isolation of the individual experience in a hostile or indifferent universe, regards human existence as unexplainable, and stresses freedom of choice and responsibility for the consequences of one's acts."