LSD (Limited Slip Differential) known in the classic car days sometimes by the brand name Posi-Trac is useful on rear wheel drive cars because it makes sure power is routed through both rear tires. Non-LSD , or Open Differential, routes power to the one wheel moving the best...but if it's moving best because it's spinning...then the car isn't moving. Therefore, an LSD makes sure either both wheels are spinning or the car is moving. AWD has many variations....but there is usually at least some portion of power being sent to the front and rear...therefore an LSD isn't as necessary since 2 wheels should be getting some power....Though If 3 wheels spin (usually only in low traction situations like mud or ice)....even most AWD systems can stop moving. (Most...not all)