How do you keep a 4L60E alive behind a modified LS?

Treat it as the light-duty transmission it is, and build it for what you're asking of it.

1. Control heat: a large external cooler. Heat breaks down the fluid, and the clutches go next.
2. Fix the weak parts: 3–4 clutch pack, hardened input shaft, beefed-up sun shell.
3. Firm, quick shifts: a valve body calibration or shift kit reduces slip and heat.
4. Match the converter to the cam; use one with an anti-ballooning plate for high torque.
5. Tune shift timing and line pressure for the new power.

	Torque it's built for	Notes
4L60E, stock	about 300–360 lb-ft (≈300–400 hp in a typical street car)	Wikipedia lists a 360 lb-ft rating; about 133 lb dry
4L65E, stock	up to 380 lb-ft	Stronger planetaries and an extra 3–4 clutch; from 2001 behind the 6.0 Vortec
4L60E, built street unit	≈450–500 hp	Upgraded 3–4 pack, input shaft, sun shell, valve body
4L80E, stock	440 lb-ft	Heavier-duty truck unit, rated to 18,000 lb GVWR (axle/vehicle dependent)

A built street unit is good for about 450–500 hp. Beyond that, see what a 4L80E swap involves.