Ah anon, good question.
*cracks nuckles* Here we go. (probably a bit too much rambling, but they are my otp, I’m sorry lol. This is going to be long.)
Honestly, I can see them as bros and/or being in a commited relationship. Doesn’t matter what kind of relationship you see them, there are things that draw them together.
First of all they’re both hella strong woman who are both so similar and yet they are so different.
They both fight for their only family they have left (Vanille and Serah) and they do everything to achive their safety. (Look at Lightning Returns - Lightning being the Savior for Serah’s sake and Fang left Vanille and went to the Dead Dunes, only to protect her from the Clavis.)
They understand eachother, their pain and they know what the other one goes through.
Lightning isn’t an easy person, especially in FFXIII. She was but a stoic soldier, not very much into emotions and the only thing she cared about was Serah and how to make the Sanctum pay. Serah was her only driving force and when she was gone, Lightning was gone too.
Fang’s driving force was Vanille and to finish her Focus. She is very loyal and sticks to her goals, no matter how hard it looks. (“I tear down the sky if it’ll save her.”) She isn’t stoic or cold like Lightning, she is rather the opposite. Open-minded, says what she thinks, kind of cocky and hotheaded.
Those two are like the same coin, but with different sides.