A highly segmented High-Purity Germanium (HPGe) detector was used to measure 241Am activity located inside the lungs of an anthropomorphic phantom with various active and passive shield configurations. It was found that the background suppression shield does not play a significant role in reducing the Minimum Detectable Activity (MDA) after veto, based on the segmentation in the depth direction of the HPGe, when measuring low-energy gamma rays. A reduction of up to 57% in the MDA was achieved. The MDA could be further improved by a thinner lateral segmentation and an optimized anti-Compton shield coupled with an active or passive backplate. The new detector application would be particularly useful in mobile whole-body counting units, where the natural background radiation poses a challenge when measuring low-energy gamma rays.