I don't think you'll get stuck for luggage charges when it's booked through another airline as part of an itinerary. AFAIK, it's only if you booked the LHR - DUB sectors direct with Aer Lingus that you would get hit

As for transfers - luggage checked through by AA should be forwarded straight over to EI at terminal 1, so you won't have to do anything. You can follow either the flight connections signs and go that way, or just exit T3 as a normal passenger and follow the signs for T1, then clear security as normal with your boarding pass for LHR - DUB and proceed to your EI flight. T3 - T1 (they're connected via underground passage) isn't a long walk really.