At the Final Fantasy Gallery event today in Japan, Square Enix announced (with English help from andriasang!)that a brand new game based on Final Fantasy XIII was in production. That game is Lightning Returns Final Fantasy XIII.
The game is being pegged as Lightning's final battle, as the character becomes the strongest she's ever been. Director Motomu Toriyama stated that Lightning had gone from a human to a God-like figure over the course of XIII and XIII-2, and that she'll be even more powerful this time.
The game is also going to be "world-driven," meaning that some form of social gaming is going to be present. That'll go over well with the fans! Lightning will be customizable somewhat, able to equip some big weapons and varied costumes, while combat will be more focused on button responses. Square Enix doesn't want to call it an action game, but it seems battles will be more action-heavy.
It'll be set in an area called Navus Partus, if that excites you.
Square Enix says more details will come later. Will she have a personality this time? Who knows!?