The discovery of gravitational waves is undoubtedly an important confirmation of general relativity. Because gravity describes our universe at large scales, it is possible to use this new experimental tool to test general properties of the universe. Among the various possible measures we mention, for example, the presence of the cosmological constant. Our purpose is to solve the Einstein equations in the Lorentz gauge in order to clarify from a theoretical point of view the interaction between the cosmological constant and the gravitational wave solution.