I do this route frequently on AA, BA and an an EXP use the BA F lounge.

However, and I stand to be corrected, without status and assuming you are in Y LGW-DUB then you have no lounge access in LGW. Coming in on an AA J seat counts for little (of course you can use the AC in DFW!) Sorry. AA don't have an arrivals lounge at LGW and BA require status or J ticket for onward connection to use Terrace.

As for clearing thing: bags will be checked to DUB, you clear custons in DUB. However you clear immigration in UK.

If you are departing DFW-LGW on the 23 of this month let me know as I am on this flight, connecting to DUB and would be happy to bring you to the BA F lounge in LGW as a guest.

edited to add: no AC in LGW anymore although AC menbers travelling outbound on AA get to use BA lounges.