I have to send TIFF files to my textile printer based on their printed color palate that use LaB. I start my designs in RBG and do the color reductions by mergering colors into an index file. The Index format does not support exact specifications. I now have to have the colors in LaB based on their color palate. How do I do that? Imagine that I'm trying to convert a Jackson Pollack painting into a restricted set of Lab colors. An individual color could be all over and in varying amounts.
Sounds like a tricky job. Contact the print vendor and ask them for a template file that includes their color palette ( swatches ). Then you will, at least, have their colors in whatever color space they need them to be. Then, I would think it just a matter of selecting and applying those colors to your artwork ( i.e., copy their file, name it, copy and paste your artwork into the copied file ).