This paper evaluates the suitability of additive manufacturing, with AlSi10Mg using the Laser Powder-Bed Fusion (LPBF) technique, for geodesic lens antennas. This evaluation is carried out with three different geodesic lens antennas operating in Ka- V- and G-band. In the Ka-band, an elliptically-compressed geodesic lens antenna was designed, manufactured and tested; in the V-band, the experimental results of a geodesic lens array antenna composed of four elements are shown. These two designs were manufactured monolithically to avoid leakage and misalignment between the plates. Finally, the challenges of additive manufacturing at G-band are discussed. A dual-polarized geodesic Luneburg lens antenna working at 122.5 GHz has been produced in three parts, so polishing can be carried out to reduce the surface roughness. The overall results corroborate that additive manufacturing with the LPBF technique is a promising method to produce metal-only solutions for geodesic lens antennas in the millimetre-wave regime.