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Photoshop can directly display the values of Lab color space or officially known as CIELAB.     Conversion to CIELCH or CIELUV is just a mathematically conversion from CIELAB so certainly could be done yet might take a script to do so.

However, simple answers to relatively straightforward questions does not solve what looks like a pretty major software development program if you are trying to duplicate the capabilities of an already existing product.   Photoshop is a very powerful program yet that does not equate to Photoshop being a good software base from which to build a product.  Just my opinion of course.