Haolepinoy is right about the hybrid LSD, so you certainly are incomplete.
The main section of the differential is a Torsen gearset which will not get a torque difference in a lifted wheel scenario. Torque sensing units allow the torque on each side to be zero even if the speed is unequal.
This is where Mistubishi added a small clutch pack to one side to accommodate the speed sensing need where a tire is lifted. Essential the wheelspin causes the clutchpack to heat and engage a small amount of torque. Once the gears get torque bias, they take over so the clutch does not bear the load. You can see the layout in the picture below. Also, in the 03+ models with traction control, the ABS system can also activate the torque bias on the spinning wheel before the clutch starts to engage. In both cases, the torsen gears lockup very quickly to provide forward motion.
I have had a 4.3 ratio Hybrid LSD in my 2005 for the last 6yrs/70k miles. It has worked very well with my traction control and has not caused any issues. It comes in handy on snow/icy roads, slick mud, and several offroad adventures. It has worked in times where I have opposite corners off the ground. It may be redundant with the traction control, but I like the added assurance of a mechanical LSD in the rear. Best practice I have found is to center the opposite corners across the obstacle and provide a slow steady throttle input while the system engages. As long as 2 corners maintain contact, I can get traction.