Well maybe this is just "sales" stuff but Leona does say she thinks the song fits for the Lightning and her struggles as a woman.

Square Promo with Leona Playing FFXIII

I know the song was not well received on the radio compared to the original theme "Kimi ga Iru Kara,” by Sayuri Sugiwara. When I first played Leono's track I did have people turn the station off, but now I can tell you I do get request for it. Not a bad track but is indeed different then what we normally expect from Square. But with the company breaking up the composer group in house I am thinking we may see more of this in the future.

If you have not seen this is the video of Sayuri from her CD single and it is kinda cool version of her just singing. She is what we expect from a Final Fantasy game but then times are changing.

Kimi ga Iru Kara - Sayuri Sugawara