Absolutely no access. Upon arrival you are segregated -- must go landside, unless you have onward boarding passes. Without a connecting flight, security will not let you through to reach the lounge. If you do manage to talk your way past security somehow, the ultra diligent BA lounge dragons will not let you in. Arrival lounges are not an Emerald benefit. If you had flown AA into LHR, where AA has an arrivals lounge land-side, you would still be denined free access (paid access is available for GBP50 for the 2 of you, much like an AC day pass); but AA has no such lounge at LGW.