As I understand it, any 308 WIN round will safely load in a 7.62x51 chamber, but the obverse isn't true. In reality, all manufactured ammo I'm aware of will fit either chamber. That is, the 7.62x51 allows for a slightly longer headspace dimension than the 308WIN, but everybody makes them to minimum specification which is well within 308 specs.My pre-ban M1A has a military TRW barrel chambered for 7.62x51 NATO. I do not shoot 308 ammunition in it.
LRB told me that their rifles are chambered for 308, so I would think it is safe to shoot 308 ammo in it as long as I stay with bullets that weigh less than 180 grains. That being said, I have only fired 7.62 NATO from it as well. Stay safe.