Suggestion for MSc-thesis:
Render a bunch of Lightroom images to JPEG while keeping the sidecar files. Then import the same raw files into e.g. DCRAW or rawtherapee, and do a brute force search to find the set of parameters that result in jpegs that most closely match the results from Lightroom. With time and patience, an approximate mapping might be found.
Using an open source developer as a "hub", all proprietary raw developers (including in-camera jpeg) could be parametrically described and transferred among each other. Probably not perfect mappings, but my guess is that mappings could be good enough that you would have a good starting point and perhaps not have to touch less critical images.
The same procedure could perhaps be used to match camera A to camera B (make the developed raw files from my Canon match the jpeg output of some Nikon camera of the exact same scene), removing raw development treatment as a source of confusion in tests of cameras.
The core issue is that no standardized exchange format for raw development processing exists (or if it does, it is not used).