I don't think AA has any codeshares DUB-LHR, presumably because they'd like you to take AA metal DUB-ORD and connect from there. DUB-ORD switches from daily to certain days and back and forth, so some Tuesdays it will not be running. It looks like you are trying to fly next Tuesday, 10/27? Unfortunately, that is a day that DUB-ORD is not running. It is running Monday 10/26 and Wednesday 10/28, so if your travel date is flexible at all you can fly DUB-ORD-NYC on one of those days.