They're called Fates, public quests that spawn all over the open-world areas of Final Fantasy XIV, and one of them has Lightning in it. Players will fight by her side against the big-ass critter in the video, earning Lightning Returns-themed gear in the process. According to the original cross-over announcement, that means Lightning outfits for the ladies and Snow gear for men.
Meanwhile, in Lightning Returns...
Pink hair and cat ears? Somebody's been reading my diary.
The Miqo'te costume and equipment based on the MMO's city-states will be unlockable in next-year's Lightning Returns via dark secrets. I shall unlock them as quickly as possible, so she is never without fluffy ears again.