You should have no problem using the BA business class lounges. You are a OW Sapphire member, departing on a OW operated and marketed flight. That's all you need.

(AA adds the additional twist that you must be on an international itinerary. But you won't have to worry about that because (a) you WILL be on an international itinerary and (b) you'll be using BA's lounges anyway, not AA's. They're in different terminals at both airports.)