im 90% sure it wont have an LSD most BMWs dont have them... if you really want to check put the car in gear, release the hand brake jack the rear wheels up and try turn one of the rear wheels...
if it turns easily and the opposite wheel goes in the other direction its an open diff...
No 328i had Limited Slip Diff as standard . Later model 6 cylinders had Automatic Stability Control .This has a seperate throttle valve to reduce power and uses ABS to stop the spinning wheel .So no lsd and asc together .