In this paper, we propose a geodesic generalized Luneburg lens operating in the 60-GHz band, from 57 to 67 GHz, designed with the goal to improve the crossover level between beams with respect to previously reported fully metallic Luneburg lenses, while providing highly directive beams and wide scanning coverage. We have combined the use of a generalized Luneburg lens and the design of a compact feeding type based on ridge waveguide in order to achieve an optimum crossover level between beams keeping in mind manufacturing simplicity. The numerical evaluation of the final integrated lens design including 21 ridge waveguide feeding ports shows a vertical bar S-11 vertical bar parameter below -13.6 dB over the frequency band of interest, a scanning range of +/- 52 degrees, a realized gain higher than 19 dBi over the whole operating bandwidth, and a crossover level value between -3.5 dB and -4.2 dB from the lowest to the highest frequency of operation.