We have simulated and measured the beam properties of lens-antenna coupled hot electron bolometer mixers at a few supra-terahertz frequencies between 1.4 and 5.3 THz. The quasi-optical structures consist of an elliptical lens and a logarithmic spiral antenna. The model used for our simulations consists of a finite-element analysis to simulate the far-field radiation pattern of the antenna, geometrical optics to map the antenna radiation to the lens surface, and physical optics to calculate an arbitrary far field. We perform a thorough study of the beam properties, such as beam waist radius, phase center location and axial ratio by varying the diameter and extension of the lens, and misalignments of the antenna relative to the lens, at different operating frequencies. The simulation results are applied to the design and optimization of three different lenses for mixers to be operated at 1.4, 1.9, and 4.7 THz, respectively, which will be used in the heterodyne array receivers on board of NASA's balloon borne GUSTO observatory. The beam properties were verified experimentally by measuring the beam patterns in amplitude at multiple planes using a heterodyne technique. We found that the experimental results show good agreement with those from the simulations. Our work has delivered the mixers with the required beam characteristics for GUSTO.