Nice idea but too unworkable in reality. You're suggesting that the lift company would put a person full time on site at T5 in order to be available to fix broken lifts. As this would not be anything like a full time role the person could be paid by BAA to carry out other routine (non lift related) maintenance?

I don't see it working. The lift company will want access to its trained resources as/when they need them for flexibility. They are a skilled resource and BAA won't pay the hourly rate for other handyman work.