Limited slip additive has one purpose. It reduces initial clutch breakaway torque, providing a more linear overall power transfer behavior. A high breakaway torque characteristic is sometimes referred to as stiction and it occasionally causes dealerships headaches from frivilous customer NVH complaints ("...I hear a noise in the rear of my car...hope it's not broken"). Performance drivers (with low torque pedestrian OEM clutchpacks) who want good 2 wheel traction should avoid these additives like the plague. Stiction (high breakaway torque) is what helps you churn both tires at launch or turn hard under acceleration. The additives reduce LSD clutch grip which adversely impacts the effectiveness of your limited slip clutch assembly. This encourages one wheel to spin under hard acceleration (more like a conventional open differential) which impedes acceleration and can reduce LSD clutch pack lifecycle.
PS: This recommendation does not apply to all racing diff's with LSD's, as they sometimes have extremely aggressive clutchpacks that require such additives to manage severe wheelhop, chatter or push/understeer symptoms.
If an LSD clutch chatters unacceptably, then you try some additive to manage it. Almost all hypoid diff lubes have enough additive in them already to manage stiction in an OEM LSD.
hope this helps
