Yes, I believe it is the groin.
I've had some groin strains and pulls before, and they really stink. It's just a nagging pain that just jabs you anytime you make a sudden turn to the side. I can't imagine what trying to play football is like with one of those things. The worst part is that it takes forever to get better...like two months or so before the pain totally stops. It's just like a hamstring pull except in a different place.
Since SD is still winning, I think they can afford to be a little less dependent on LT. That isn't good for fantasy owners, but it gives him a better chance to play in every game and contribute.