It sold double, but it still underperformed at retail. Estimates were 6m and it sold 3.6m. This means that they may not have planned a sequel, in which case MS may have funded it themselves or part funded development, just like they did with Titanfall.
http://uk.ign.com/articles/2013/04/09/square-enix-reveals-sales-expectations-for-tomb-raider
If so, why did it get announced at E3? That suggests it was already in production. And if they knew it was already going to be exclusive, you can be sure MS would have announced it loudly at E3