I think I wrote over 400 pages of technical reports while at Kodak on this, just on how to build, use, populate, estimate, validate, visualize, all applied to 3D luts. :) Plus two US patents on the subject, that should now be expired, at least given the application dates.
There are many possible schemes to populate n-d LUTS, some more viable than others. My gridfit tool (on the file exchange) is essentially one of them, although it is limited to 2 independent variables, thus only 2-d luts. (When I wrote gridfit, my patents on the idea were not yet expired, so I chose not to write it for higher dimensional problems.)
Don't forget there are often issues with color & device gamuts when populating these luts. In fact, I invested man-years of my career in developing methods for gamut mapping. Lots of interesting issues there to trip over, but also some pretty mathematical approaches.
In terms of a tool that can be simply used to solve your problem, since my old tools for 3d LUT estimation are not in the public domain, I'd suggest you might look at the 3-d inpaint NaNs tool I wrote. It too is on the file exchange. You would need to replace the empty cells in a 3-D array with NaNs, then call the tool three times, once for each output channel of your 3D-LUT. The method used in that tool will be important. Thus, to avoid extrapolation, use method 1: the 'springs' option.
Again, beware gamut issues.
