You need it to be a single booking to get checked luggage to go through to DUB, both for AA and BA ticketing. Two tickets means a re-check stage, and so you should allow more time. In theory, with the new e-gates, a 90 minute connection could work, but it gives little leeway for delays. Depending on the consequences on missing the flight, I would say 3 hours would be better. You would also have to go landside rather than do an airside transfer, since AA use T3 and BA use T5. Aer Lingus (codesharing as BA perhaps) use T2. Generally through tickets to DUB from the USA are cheaper than LHR, so that's a bit unfortunate, I wonder if you need to dig a bit deeper into the booking process to come up with a cheaper ticket.