I would watch the arrival time of AA135 from LHR. If the arrival time is close to scheduled time at 8:40pm then I would not assume AA can really turn the plane around in 90 minutes.
I would give them more like 2 hours so I would guess more like a 10:45pm-11pm departure.
Maybe realistically plan on a 5:30pm arrival or so.
You could probably then make the BA at 7:05pm still without a problem.