I don't know what BA's specific policies are, but here is the oneworld policy:

"Emerald and Sapphire members may invite one guest to join them in the lounge. The guest must also be travelling on a flight operated and marketed by a oneworld carrier. You must be prepared to show your boarding pass and frequent flyer membership card, with oneworld Emerald or Sapphire tier status, to access a lounge. Access is available on the day of travel (or before 06:00am the following day), at the airport from which the oneworld flight on which the eligible customer is travelling departs."