Re: DC's New 52: Reviews and Discussion (Spoilers welcolme and likely)
I'm pretty sure that War was before New 52, and that we essentially have a continuity problem. There was never a single moment between Hal getting a ring from Sinestro, and his "death" by Black Hand for him to spend any time running around with the League.
"In Brightest Day, in Blackest Night, no evil shall escape my sight. Let those who worship evil's might, beware my power: Green Lantern's light!"