Reverse-engineering the development parameters of common raw developers would be an interesting task, and might allow a coarse conversion of the kind asked by the thread starter.
Say that you set C1 and Lightroom to "standard neutral", compare the results for a bunch of raw input files, then have a program search through all parameter settings to find what settings make Lightroom most "similar" to default C1.
Once this is established, you might change C1 parameter settings one at a time, and in groups, and do the same to see what Lightroom settings corresponds to a given set of C1 settings.
Similarity could be a simple or advanced metric but would probably only correlate to a degree with what you and I might think.
Sounds very time-consuming, but for a computer that never gets bored, this might be doable. There might be a tremendous speed-up if some expert guided the algorithm in hinting that fiddling with Lightroom sharpening settings probably would only affect the curves/levels to a minimal degree and might be excluded from the corresponding search.