Lyndonville NY is a Census "Place" geography NY FIPS = 36 Lyndonville Village Place FIPS 43918
. I'm going to answer your Van Nuys CA question here. The Web page that I gave you a link to gives their methods which you can program yourself once you have a shape file for Van Nuys. I was not able to find a shape file for that neighborhood but if you email Los Angles county you can probably get an "official" shape file. Then sum up the tract populations for tracts that are inside the neighborhood boundary. For tracts that span the boundary use the proportion (by area) of the tract population that falls inside the "official" boundary given by the Los Angles County map/shape file.
I use R which uses the libgeos C++ library (open source) https://libgeos.org/ (R rgeos and sf packages) It computes intersections, areas etc etc.s
Dave