Not enough information to determine here

BA LHR-DUB, in what class? If its flagged as Club Europe then you have access to the T5 BA Galleries lounge, if not unless you have BAEC Silver or oneworld equivalent or better you won't have access
EI DUB-PHL, access on basis of class of travel at the 51st and Green lounge and the slightly faster screening queue at US CBP at Dublin, while you have access to the normal Aer Lingus lounge the staff will direct you to proceed to the US immigration and then 51st and Green


For future reference if this was ticketed and flown on EI entirely, you would have access to the lounge at T2 LHR