TC is independent of the rear differential configuration. Traction control is an electronically controlled feature that uses the wheel speed sensors, observing any delta from the rear wheels spinning faster than the front wheels and or one side versus the opposing. The control is normally done electronically at the throttle body decreasing power commanded, and pulsating the brakes, thus retaining traction.
Limited slip is a mechanical function, the limited slip clutch pack attempts to keep both wheels turning at the same rate. Once the torque side to side is greater than the clutch pack can maintain, the wheels are able to turn at different rates, such as navigating a corner.
A locker is either engaged keeping both wheels at the same rate, or open, just like an open differential where the wheels are free to spin at different rates and are operating totally independent.
Ford's less than optimal implementation of the locker (electronic) only engages manually via the driver pulling a knob. This is unlike the GM G80 mechanical locker which automatically engages when 1.5 rotation difference occurs side to side.
TC and a LS or locker both are all attempting to solve similar problems through different means. The combination of these complementary systems is better than one system alone.