A broadband terahertz (THz) quasi-optical detector based on 3D-printed lens packaging has been presented, covering two typical atmospheric windows at 220 GHz and 340 GHz. The detector consists of an antenna-coupled detector chip and a 3D-printed lens. The antenna-coupled detector chip was packaged on the multi-layer dielectric laminate with the Schottky diode directly integrated across feeding terminals of the chip-on antenna. Patterns of the on-chip integrated broadband planar bowtie antenna were printed on a quartz substrate within the frequency range of 201-405 GHz, serving as a radiator and a radio frequency (RF) choke. It utilized a pair of capacitively loaded loop (CLL) to broaden the operational bandwidth, while essentially maintaining the overall antenna dimensions. Additionally, well-designed high-impedance folded low-frequency (LF) leads were integrated for achieving effective signal isolation and radiation coupling characteristics. To achieve unidirectional antenna radiation patterns and enhance the overall structural mechanical robustness, a lightweight and lost-cost 3D-printed lens combined with metallized reflector buried in multi-layer dielectric laminate was proposed. The detector exhibits a maximum voltage responsivity of 2200 V/W in the 200-230 GHz range, and 1885 V/W in the 320-350 GHz range. The measured radiation patterns show good agreement with the simulated results.