AA also has a lounge at FRA (the AC outside of security) and it happens to be the best OW lounge at FRA (better than BA and CX). None of the lounges are very good at FRA, if you need a good lounge the best choice is to either fly LH in F (then you can use the separate F terminal and that does have a good lounge, best in the world at the moment) or pay to use the Sheraton hotel facilities.