Both are in terminal 2A. You do not have to clear immigration nor the main security, but there is a separation of incoming and outgoing passengers and the only way to either go to the lounge or simply find anywhere to sit is to pass that separation. You will have no problem doing so by asking the agent meeting the incoming BA flight. You may have to go through a side security point, as this is the purpose of separating inbound and outbound passengers. This should be very quick. IF nobody meets the BA flight (I have seen it), there is a connecting counter next to immigration. This should be very quick.