It really depends on the tire.
I've run Michelin Pilot Super Sports past the wear bars and they were still okay, even on a wet road. The only reason I replaced them was either an inspection coming due, or that I just didn't want to wear them down to the cords.
Cheaper tires have always fared worse. The worst was a set of Falken FK452s, which I pulled off my old car at half tread depth because the NVH was literally intolerable -- as in, they turned a car I loved into one I literally disliked driving.
My most recent set of winter tires were pretty much done once they got below 3/32". Not much use in snow, and a bit pucker-inducing under braking on a wet road.
Most longer-lived tires will actually age out before they get near the wear bars, not to mention having pretty poor grip even in the best of times. I'd think tires like that would be pretty scary at low tread, even on a bone dry road. Then again, tires like that scare me even when they're brand spankin' new, so maybe I'm not the right guy to say.
I don't think any tire is going to perform "to spec" at 2/32" or 3/32". The question is whether they'll work well enough to give you the safety margin you want. Without knowing the LTX M/S2 specifically, I'd guess hydroplaning resistance would kind of suck, but traction on a simply damp surface should still be reasonable. But it's your judgment and your call.
