Aside from Cloud Strife's costume, Lightning will also wear Aerith Gainsborough's costume from Final Fantasy VII in Lighting Returns: Final Fantasy XIII! Below is a video featuring Lightning wearing the said costume.
Aside from Aerith's trademark pink dress, she is also equipped with a shield that looks like Aerith's flower basket and Aerith's Guard Stick. This costume can be acquired as a bonus that comes with an issue of V-Jump magazine.
As of this writing, there are no plans if this costume will be available outside of Japan.
UPDATE (9/25/13): Square Enix Europe posted a clearer version of the Aerith promo. Details on how players can unlock the costume are still unknown as of this writing.
[Source: Siliconera]