The claim that the best interpolation kernel for 2d images is just a product of two Lanczos kernels in the X and Y directions seems wrong to me. Rather, there is a proper 2D analog to the sinc function known as the jinc, or "Sombrero" function https://en.wikipedia.org/wiki/Sombrero_function . (This function is mathematically related to the "Airy" ringing patterns found in the optics of lenses.) Resampling with a jinc-based circular-window kernel should show a far lower intensity of ringing artifacts compared to the simple composition of two 1D Lanczos filters.

On a different point, when approximating a "brickwall" frequency spectrum an 'equiripple' pattern is generally considered desirable, and this will lead to a different kernel than the Lanczos approach does.