I guess it IS all about traction. Traction in the corners and when wet/slippery/snow. IF you feel that you would really gain from an LSD... go for it.
It is not gonna be cheap at around +$2K. You have a few things in your favor... that auto trans means your ring gear is a bolt in... so its way less labor for the install then a welded unit that the manuals have.
I would contact VAC Motorsports in PA or Harold in CA. Those two have the most experience in LSD installs - I am sure they must have done one already for a 128i. Please post and keep us updated.