I don't have limited slip but I do suffer from the all-to-common rear end whine. I filled with one bottle of Ford's heavier diff oil and a bottle of Lucas oil treatment. The whine is about at 1/3 the level it was before. Better than I expected.
Lucas states that one could use their "additive" exclusively in a diff. Not sure if this would result in better performance or a quieter ride.
Also, the stuff is a real bear to pump due to its honey-like viscosity.