F20 + 300ft/lb = It will die after a while.
F20 + 300ft/lb + LSD = It will die very quickly indeed.
Loss of traction means the torque is not applied to the gearbox. You increse traction (slicks, LSD, whatever) then more torque will be applied to the 'box.
This is why on big power conversions it's the higher gears that go first as wheelspin is less in them. Nothing for the engine to work against = no torque produced.