Lowpass Lanczos filter
This is a rather late response, but I just came over this question. So if it could of any help to future problems for anyone, I will post an answer:

Although your question is pretty comprehensive; In my experience with the Lanczos filter, it is a rather versitale filter especially when it comes to image processing. I have mainly used it for scaling images, where the filter is a part of other FIR processes. To use it I would design the Sinc function(which is defined by the Lanczos resampling function) to be dependent of the following parameters: Upscale factor (N) and filter order (a). When I defined the window length it is a simple function of the two parameters which is:

k = (a * 2) + 1


and then the window space results in:

x = np.linspace(-a, a + (N-1), k*N)


where k*N is the length. The Lanczos Sinc function is then multiplied with the interval values. 
This was to give a practical example. In other words, you need to know what you want to do with the filter. It is highly dependent on what you want to filter, and you need to define one (or more) parameter, besides the filter order, to define the actual window length to take full use of the filter.

To give a quick overview of the Lanczos:

It is just one of many ways to realize the Sinc function in practical terms, and it is quite good when it comes to image sharpening and interpolating between resampled discrete data points.
It does have some limitations though. If the range of values of the interpolated signal is wider than the range spanned by the discrete sample values, it can cause ringing artifacts which ultimately leads to clipping artifacts. However the effect of this is quite low compared to many other realizations of the Sinc function.