The Luneburg lens is widely applied in both the optical and microwave regimes because it offers high gain and a wide beam-scanning range. However, Luneburg lens typically suffer from low efficiency which is caused by the dielectric loss of medium employed. To address this issue, we propose herein a general method for discretization of two-dimensional Luneburg lens based on correctional effective-medium theory. In discrete Luneburg, the efficiency is not dependent on the employed medium roughly because that the main component in the lens is air, resulting into a significant improvement of efficiency. Subsequently, a systemic study of lens discretization is presented, which is validated by a discrete Luneburg lens easily fabricated by using 3D printing. In addition, a novel wave-patch reduction feature allows the discrete lens to function as well. This work presents a fundamental theory for lens discretization, which is valid not only for the Luneburg lens but also for other types of lenses. It can be applied in imaging, antennas, or phase manipulation in both the optical and microwave bands.