Artificial dielectrics are widely used for Gradient-Index (GRIN) lens antennas. The unit-cell size of an artificial dielectric determines the maximum operating frequency and also drives cost and yield. To explore the frequency limitations we printed four identical Luneburg lens antennas using gyroid unit-cells of 12.5, 10, 7.5, and 5mm and measured their gain over the K- and Ka-band. We find maximum frequencies of 20, 25, 33, and >40GHz for each unit-cell, respectively. These measurements suggest a print resolution limit of $0.7λ_g$, where $λ_g$ is the wavelength in the host dielectric.