IIRC, they are rated at about 2000lb. This is approx what the per wheel loading was on the tow truck at failure. This is not significantly different load than when we dragrace with them on the trucks. Front tires see about 1900lb, rears about 1500lb.
The following is dragrace/AutoX experience, not LSR (yes, certain DR's are excellent AutoX tires):
I've run several different brands of DR's or DOT bias-ply slicks on the street and track on about a dozen late-model vehicles.
Stories about quick failures are not unique, and even happens in lightweight cars like Corvettes. Some have reported failures during long-range sustained freeway driving or greatly accelerated wear (cord them in 100mi). Nitto DR's or BFG's are fine. But the really soft DR tires like M/T, Hoosier, or M&H don't seem to like long range.
I suggest if you dragrace with these kinds of tires, limit yourself to 20 miles drives to the track or change them at the track. Regardless of the DOT rating, they really aren't street tires. They are drag slicks with rain grooves (oh, they seriously suck in the rain even when new).
As far as LSR goes, I personally wouldn't run them on a long course especially with a lot of ballast, but that's just my personal opinion. Nitto's AOK since they are a much stiffer tires. BFG's are AOK as well.