In this letter, we present an additively manufactured half-Gutman lens antenna operating at 30 GHz. The hemispherical lens allows for a compact beamformer while maintaining the wide scanning capabilities of Gutman lenses. This solution further enables to better integrate the feed system when compared to a more conventional half-Luneburg lens antenna design as the focal arc is moved inside the lens. The graded-index of the lens is implemented with a periodic structure arranged in a body-centred cubic (BCC) lattice. We demonstrate that the BCC structure provides attractive properties for the design of inhomogeneous dielectric lenses. Importantly, the BCC structure can be used to alleviate the manufacturing constrains compared to conventional periodic structures. The lens is fed by a dielectric-loaded square waveguide. The proposed antenna produces a directive beam with a simulated and measured peak gain of 26.2 and 25.3 dBi. The antenna can steer its beam in a 50 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula> range in elevation with measured scan loss and sidelobe levels below 1 dB and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-$</tex-math></inline-formula> 10 dB, which agree with the simulated values. The measured cross polarization discrimination is better than 20 dB. The proposed antenna is intended for the ground segment of the emerging low-Earth-orbit satellite communication applications.