Final Fantasy XIII's Lightning has appeared in Realm Reborn's Eorzea, and she's snatching a costume for the trip back to Nova Chrysalis.
The Final Fantasy series is known for many things, but outside of an impressively misleading title, it's usually known for featuring a new fantasy universe in subsequent game. Barring obvious sequels like Final Fantasy XIII-2, each game features a new storyline and set of characters that rarely overlap with the others. Note that I said "rarely" instead of never; one example of a recent crossover is occurring right now in Final Fantasy XIV: A Realm Reborn, as players can now fight monsters alongside Final Fantasy XIII's Lightning.
If you've played Final Fantasy XIV: A Realm Reborn at all, then you're probably already familiar with the game's FATE battles. If you haven't, FATE (which stands for Full Active Time Events) refers to periodically generated events across Eorzea that players have a chance of stumbling into. One of these events now features Final Fantasy XIII's Lightning, who supposedly crossed through a dimensional breach, letting her fight monsters alongside your party. Players who participate in Lightning's FATE battle will be rewarded with gear and weapons from Lightning Returns: Final Fantasy XIII.
The crossover appears to even have effects on the Lightning Returns title. Square-Enix has released screenshots of Lightning wearing a Realm Reborn Miqo'te costume within her own game. Clues will be scattered across the world Nova Chrysalia for players of the title to find.