T3 definitely have access to sky, but whether they will readily switch is another thing. I would recommend requesting through the BS supervisor at the time. After a quick shuffle around the AA lounge last week, I did not notice any sky available, but that's not to say there isn't. I do agree that after testing, the AA wifi is much faster. The BA wifi tends to be weaker along the back wall of the lounge in proximity to the rear toilets.