You said you went on bmwusa.com and saw the LSD it states that it is electronic( so I thought you meant is it going to come with the car). It will come with an electronic lsd, So no it is not a real lsd.
When one wheel starts to lose grip it applies the brakes to the wheel that needs it. I believe it is standard on 135i, not sure about the 128i....
I never said it will have a true lsd I said electronic