Both the 97' US spec C36's I've had, no LSD. I believe the ASR was in place to correct traction.

And I have yet to come across anything in the US with LSD.

Only my 211 E55 had it installed after later on as a upgrade.

I always had my eye out for a BMW E30 325is 3.73 LSD because they looked very close in size as well as someone telling me the axle bolt patterns were the same, all I'd have to do is fabricate the diff mount points and convert my driveline to U-joint instead of rubber disc. Just a rumour.