No they are not designed overnight but Ford had LR for four years before the D3 was in the showrooms.
It's logical to say that BMW would be putting the sale of LR in motion years before that, and so wouldn't be investing in a engine for a vehicle that won't be built fo years to come.
Fours years is long enough for giant company like Ford to design a vehicle and engine, so it's doubtful that it's a BMW engine, or even a BMW part finished designed, if what are your asking.