The 190E 16v uses a limited slip. You'd be better off getting one of those. I will eventually be putting a 16v LSD into my coupe as both have nearly the same final drive (3.06 coupe vs. 3.07/3.27 16v). Only thing I'd have to do to make it work is possibly modify driveshaft (yokes may be different) and swatch out the rear covers.
Only LSD diffs the 124's had were the ASD ones Paul mentioned. those were available in the E320/420/500 and some diesels.
I can only just imagine how an 8valver would behave with an LSD. the little 190 5 speed i have was VERY fun even with an open diff.
