BA have the resources to re-train you very quickly onto whatever they need. If you hold a 757 rating then you qualify for ZFT onto the Airbus thus negating the need for costly base training.
The last 757 goes out of service next month and the hull reduction means there are plenty of surplus pilots for the 767.
Just to add a little, if you are desperate for LH and join DEP on the 777 then you will be at the bottom of the seniority list. As those who joined prior to you on the SH roster come up for fleet transfer they will join the seniority list and thus the bidding list ABOVE you, pushing you down further. Not a nice place to be for 5/6 years as some of the junior FO's who were DEP onto LH in the last recruiting phase have discovered.