Will a 4L60E bolt up to a 5.3 or 6.0?

Yes, an LS-version 4L60E bolts to any Gen III/IV LS engine (5.3, 6.0, etc.). LS applications use a 300 mm input shaft and LS-specific converter; the older non-LS 4L60E (e.g., behind a 4.3 V6 or small-block 350) uses a 298 mm input shaft, so reusing one on an LS needs the matching LS torque converter/crank setup.

Strength-wise, a stock 4L60E is comfortable around 300–360 lb-ft (≈300–400 hp); built units handle 450–500 hp. For more power, look at the 4L80E (440 lb-ft rated) or 6L80/6L90. The transmission also needs control: a factory GM PCM that supports it, or a controller like the Holley Terminator X Max.