If BA had to take Baby with mainline in order to secure the deal with LH, BA will have to do something with it. However, having thought about it I simply can not see Baby being integrated into Vueling. Yeah Vueling is part of IAG, but seriously the UK has the most competitive low cost operations, well certainly more carriers in a crowded market place. FR, LS, EZY etc. etc.
Personally, I think it would be a mad idea to place Vueling in the UK where Baby is now. There are far more places on the continent that would make more sense.