Been through AGP countless times over the years. The Sala VIP lounge is operated by the airport and can be accessed by departing pax by turning right after security and then walking several meters down to the entrance on the right. It serves several carriers that depart from T2.

BA (actually GB Airways) will issue an invitation at check-in if you have eligible OW status (Sapphire, Emerald) or flying Club Europe. IB has never issued me an invitation but I have always been able to access the lounge by showing a BP that has my OW status printed on it.