If anyone knows how to in P/Shop (...) please let me know
Process capture. Process LCC shot with the same settings (white balance, icc profile). Open capture in PS, add the LCC shot on a second layer. Invert second layer with the LCC shot and set layer mode to "overlay".
edit: sorry, forgot about the 50% grey... so...
1st layer: capture
2nd layer: create new, mode "overlay", select "fill with 50% grey"
3rd layer: LCC shot, set mode to color
4th layer: merge 2 and 3, invert, set to "overlay" and delete or turn off layer 2 +3
Without the 50% grey vignetting is corrected as well.
With the 50% grey just the color cast is corrected.