Ripple in time-domain using lanczos resampling
Figure 1. Illustration of the problem with Lanczos2 interpolation: The sum of the four time-shifted Lanczos-window multiplied sinc functions (red) do not sum (black) to unity in the middle between horizontal coordinates 1 and 2.

A simple fix would be to distribute one fourth of the deviation from unity as function of the fractional position in the middle interval, with negative sign, to each quadrant of the Lanczos2 kernel. The equations are lengthy, but this is all very easily done numerically. The difference to the original Lanczos2 kernel is small:

Figure 2. Lanczos2 kernel (blue) and fixed Lanczos2 kernel (red).

Figure 3. Fixed Lanczos2 kernels (red) sum to unity (black).

The magnitude frequency response from the fixed Lanczos2 kernel looks just fine compared to the original, by some measures even better:

Figure 4. Magnitude frequency response of Lanczos2 interpolation (blue) and the same with the fixed kernel (red).

A similar fix could be tried on larger Lanczos kernels. I tested it on Lanczos3 and saw no problems.