The factory LSD is the Trac-Lok. It's a clutch and spring type LSD.
Actually, the question isn't how/when it engages. It defaults to being "engaged." If the torque delivered to each rear wheel differs by more than a certain amount, then the clutches slip and allow the differential to ... ahh... differentiate.
So -- if both rear wheels are in mud or on snow or ice, traction is approximately equal and both rear wheels will drive. Put one wheel on dry pavement and one wheel on ice, and the potential is there for a difference. Under light throttle, torque will be delivered equally to both wheels and the wheel with traction will drive the vehicle. Mash the peddle hard enough, though, and if the wheel on dry pavement has enough "bite" the torque bias will exceed the clutches' capacity and the diff will release.
That's also what happens going around corners on dry pavement. The outer wheel generates enough torque relative to the inner wheel to cause the clutches to slip while rounding the corner, thus avoiding tire squeal.
Help any?