Matt - I've been a Terminal 1 commuter in DUB for the past 15 years on a weekly basis so know the airport and procedures better than most.
The aircraft operating your LHR DUB will be the aircraft bringing you back to LHR. I feel like I know some of the crew better than my own family! They are extemely used to back to back at DUB therefore make sure you tell them you are back to back whilst in flight to DUB. Routinely they tell the gate arrival agents (who dispatch the LHR sector) that Mr. Matt is a back to back "runner" to security. At Online Check in get an aisle seat LHR DUB as close to the front in economy so you deplane quickly. Clear Immigration - Common Travel Area check and very swift. My advice (irrespective of any other advice) is to exit customs via the blue channel into the public arrivals area. Please ignore flight connections. Make sure you have DUB LHR boarding pass on App / paper so you don't collect it in DUB.
Once public - turn right, up escalators and walk past check-in area 4 (BA Zone) directly to Fast Track which is usually quiet. Once clear of security then turn right and immediately left - upstairs to DAA lounge where the very warm and welcoming staff will greet you awaiting your return flight. I would expect 12 minutes deplaning to DAA lounge and that's moving slowly. It is in no way dodgy.
On your return back to DUB from USA - 3 hours is fine. BA flights almost exclusively leave from gates 301 - 304. I have had a series of delays on LCY services recently which puts your connection to EXT at risk if it happens. In fact I have recurrently been TP across to LHR services by the ticket desk due to late LCY services.
Hope this is useful and have a good trip!