Asymmetric-dual-grating-gate high-electron-mobility-transistors (ADGG-HEMTs) are expected for high responsivity, room-temperature operating, and high-speed THz detectors. However, their low light coupling efficiency is one of the serious concerns because of the large focused spot size of free-space THz waves. To improve this, we examine shrinking the THz wave spot size by integrating a detector with a hyper-hemispherical silicon lens. We report the 6-fold enhancement of the coupling efficiency by the silicon lens integration. Also, we show that the dependence of the detector module responsivity on incident THz wave frequency is given by the product of the internal responsivity of ADGG-HEMTs and the light coupling efficiency owing to the silicon lens.