I'm with Kagari--I feel like Lightning was a character who was conceived to be directed towards 20-something females (possibly in an older sibling position), but she ultimately didn't deliver on that front. At least to me, she didn't. Lightning kind of lacked the emotional scenes that allowed you to easily empathize with her or to identify with her as a multifaceted character who isn't just there as a character whose sole purpose is to look cool or to let her fists do the talking. There is a person behind those fists and I'd like to know more about her. But I didn't get to know much about her.
At the end of it all, I feel rather disappointed with Lightning's execution. As a female and (probably overprotective) older sister, I had something additional to look forward to in a Final Fantasy: another female protagonist, whom I feel like I could somehow empathize with, easily acknowledge her personal struggles, and feel like I could walk in her shoes. Someone who isn't just an aggressive soldier in a miniskirt, but someone with emotions that I could easily relate to. While Lightning probably resonated with other females (in this very thread, even), I feel like she didn't resonate with me as a result of being rather one-note. I feel like I resonated more with Vanille and Fang than Lightning.
It's kind of funny... I felt like I resonated with Fang (a character whom I also consider to be rather one-dimensional), who's Lightning's foil. Fang's plight mirrors Lightning's in a way (she's out to find and save someone important to her, someone whom she'd considered as her sister (or whatever you wanna think they were)) but what Fang had was small development with Vanille... and Vanille had a lot of development in that game via game narration, her chapters with Sazh, and her story with Fang. Fang somewhat benefitted from Vanille's story and execution, but Lightning's story somewhat suffered because you merely had short flashback sequences of her yelling at her sister for being a fool, the intro sequence that took place in media res prior to any flashbacks, and maybe some of her conversations with Snow. But after all of that, I feel like I didn't understand her or could empathize her in some way. I know that some other people could totally understand and relate to her, but I felt like I couldn't. By comparison--if I really needed to do this--I felt like I could understand Celes, Sarisa, and Yuna a lot more than her because they had the backstories, character interactions, and character relationships to back their personalities up.
If you'd read the prequel novel prior to this, you'd see that the Farron sisters are somewhat closer than this, but if you merely go through the game without reading any of the supplementary (near-essential) materials never released in English, you aren't going to get much out of the Farron sisters' relationship. They tried to rectify this with FFXIII-2, but I ended up enjoying and understanding Serah as a character far more than Lightning.
