It’s more like the L is an intensity/brightness factor, and then the a and b values corresponding to the two dimensions of opponent color that neurons capture in the thalamus one step after the eye
So, sure, this "4th dimension" (for normals) might be as simple as "candelas" - truly orthogonal, but one does hear an awful lot about "ambient" or "candela contrastive" (a term I just made up) kinds of effects. (EDIT: e.g. in color calibration of projectors in dark rooms vs. living rooms, for example, but I'm sure there are many.) I am just one person, but it feels like candela brightness matters for color perception. So, maybe luminous intensity is not actually exactly orthogonal. Maybe this is all covered in the 1931 CIE documents, though.