Both flights operate out of the North terminal. They will need to clear security but they won't have to go through customs nor collect luggage. LGW transit is not nearly as bad as LHR.

AA50 on-time arrival for the last 2 months is 55%, with an average delay of 47 min. The minimum legal connection time is 60 minutes, but from deplaning to the connecting gate should be about 30 min. Their transit time is 65 minutes, and that doesn't leave much time for delays. AA's record on this flight is not too encouraging. BA2540 has an on-time arrival of 63%, with an average delay of 19 min.

If the LGW connection is missed, they will likely be placed on the 13:55 BA flight to FCO.