If you have spectral data, and you want to graph it, then it seems wrong to map to CIELAB space. The spectral data has infinitely more information (dimensions) in it, and you throw all that information away when you map to the 3-D CIELAB space.

The same is true for a mapping to RGB space.

What are you trying to accomplish? Maybe something like the graphs shown in Figure 2 of this paper: http://papers.cnl.salk.edu/PDFs/The%...02000-3503.pdf? Note that the paper is an arbitrary one that I found in a quick search for graphs of spectral data.