We need a bit more info. Year and engine would be helpful, but what we really need is to know what you mean by "will give out completely" and what the circumstances are when it happens. F'rinstance, does the pedal go all the way to the floor, or does it pulsate, or does it feel fine, but the car seems to take a long time to stop? Also, how were you driving when it happened? Were you autocrossing, or in heavy stop and go traffic, or did it just happen all of a sudden (ie, you stopped at a stop sign, then the next one you rolled through)? Can you replicate the problem, or does it just happen randomly?
One thing to keep in mind, if you're new to the LS, is that its near 50%-50% front to rear weight distribution and its anti-dive/anti-lift suspension geometry can make its braking performance deceptive. It doesn't pitch forward like most cars, so it can sometimes seems like it's not braking well when it really is.
If you can flesh out the story a little more, I'm sure we can help...