There are issues associated with this change
1. There is no ready made LSD kit available for DANA 44 / 19 spline axle
2. The currently available MM550 LSD (Trac-Lok) is matching to DANA 44 differential but spider side axle spline count is 30 against 19 in Classic
3. The axle track of MM550 is not same with CL340 DP - Classic, as heard from experts(CJ/CL 340 = 48 inches, MM540 = 51 inches and NGCS MM540 = 53 inches). but I have not measured the size of MM550 and Classic axles yet.
With the above constraints, I have few options to implement LSD setup on my Classic
1. Take the complete differential setup for front and rear from MM550 and use it in Classic
2. Take only the LSD from MM550 and custom fabricate axle to fit Classic axle length setup, this exercise may lead me to convert the semi floating axle to full floating type (Though bit tricky but I know a expert who has done it for his Jeep earlier)
3. Buy a on the shelf Dana 44 / 19 spline Auburn Limited Slip(http://www.drivetrainwarehouse.com/PDT259648.aspx) from overseas and get it installed in the existing housing and axle setup.