I'd be far more worried about the added stress on the transmission and torque converter (until you re-gear for the tires), than the LS and differential. As mentioned, the limited slip is a clutch type that is prone to wear no matter what. Larger tires could wear it faster in theory, but unless you drive your truck like you hate it I don't see it being an issue.

As for Chevy's exploding their rear axles... the older Chevys had a terrible 8.5" 10 bolt rear end that was not of good design. The 9.5" 14 bolt rear ends on the other hand are a good match for the 9.75" Sterling/Ford in terms of strength.