UA & EI are friendly these days; can anyone clarify the UA lounge relationship?

I am flying United issued ticket with UA ORD-LHR paid J EI LHR-DUB paid Y. According to my reading of post 1, I would qualify for lounge access in LHR under the provision "Passengers travelling on Flexi Fare (within Europe)."

My return is EI DUB-LHR discounted coach, UA LHR-ORD paid J. Will I qualify for lounge access in DUB under the provision for "Passengers travelling in Business Class (trans-atlantic)" or will my *G be sufficient? Alternatively, my flight is not booked as a BA codeshare, but also carries a BA flight number. Can I gain access as a BA Silver?

Thanks for the clarification.