In this paper, a novel dual-slant polarized three-dimensional (3D) periodic Luneburg lens with a diameter of 390 mm ( $4.6\lambda{0}$ at 3.55 GHz) is presented. Copper-plated cubes with truncated corners are placed in a body-centered cubic (BCC) lattice and held together with layers of Rohacell foam. The sizes of the cubes are varied to realize the gradient refractive index (GRIN) profile of a generalized Luneburg lens at a low cost, with a low weight and loss. The designed Luneburg lens operates from 3.3 to 3.8 GHz with a total weight of 1 kg. The quasi-isotropic response of the proposed periodic structure allows a wide angle coverage. Measured results show that the lens antenna can achieve a peak gain of 22 dBi with a scanning loss of less than 0.4 dB in a wide angular range in both the azimuth and the elevation plane. Importantly, the proposed lens antenna design achieves a cross-polarization level below peak gain of less than -19 dB at all angles for the two slant polarizations of the feed, while comparable designs report up to -11 dB at given angular directions. This high-gain multi-beam antenna with a commercially viable design is suitable for wireless communications at low microwave frequencies.