This paper presents a terahertz beamforming network based on a nonlocal lens with a 2D beam-scanning demonstration through leaky-wave antennas. The proposed design methodology is novel, to the best of our knowledge, in the aspect of using unconventional optimization parameters to significantly reduce the phase error associated with this class of beamformers. In this approach, a nonuniform contour defined by Fourier series expansion is used as a new optimization parameter to significantly decrease the phase error over a larger scan-angle than that in the previous works. The proposed system is a good candidate for industrial and security applications such as automotive radar sensors and electromagnetic THz imaging, thanks to its extensive 2D scanning range: -68∘ to 0° in the elevation plane and -45∘ to +45∘ in the azimuth plane over the frequency range of 140-180 GHz.