What's Your Angle?
"I was born into a Fal'Cie world, raised on a Fal'Cie leash.
Without a master to follow - my life had no purpose."
I believe Lightning is motivated by a desire for power, but not in the typical sense. Most people want power for shallow, materialistic reasons. Light thirsts for control, control of her own unpredictable life. This is similar to the overall theme of the game, which is something like "resisting the world" or "taking charge of your fate, not being a slave to outside influences." Thus, Lightning is a suitable protagonist because she has ALWAYS personally desired this freedom. This motivation is the cause of everything, from her name change to her aversion to weakness.
the origins
That day, the moment she was held by her mother like a small child, her childhood was over. She no longer had anyone she could call mother. So she was no longer a child. Could no longer be a child.
Part 1 of the novella FFXIII Episode Zero gives us a peek at Lightning's background. Her father died early on. Lightning comments that she loved his easy-going nature then, but would have disapproved of it now if he had lived. When the Farron sisters were barely in their teens, their mother was dying from an illness. At her deathbed, Lightning's mother told Light that things would be different soon, but that Light and Serah should support each other. Lightning didn't listen, she believed that she really had to carry a burden all on her own. On her mother's grave, she took a new name.
I want to be an adult. She felt it keenly. To protect Serah, to make my only little sister happy, I have to become an adult as fast as I can.
Wanting to grow up faster is a common thought among adolescents. However, Lightning took it to a higher level. The passing of her mother during a pivotal stage of Light's development kicked Lightning into an unstable place. Despite special programs that would have taken care of the two, despite the presence of a strong sister to lean on, Light felt she was all alone, and she had to become strong all by herself. She couldn't see any other way. She based on her idea of an adult on her mother, who worked a lot after their dad passed away. She gave herself an identity too: the only person who can protect Serah. It was the same identity that her mother had before her.
her mentality
The advice that Lightning gives Hope reflects Lightning's actual philosophy in how she lives her life. Here it is: (Excerpt from a conversation in Gapra Whitewood)
Control your emotions. If you want to survive, you forget about sympathy. How can I explain? Think of it like a strategy. Focus on your ultimate goal and shut out everything else. Still your mind. Move on instinct. Let doubt take over, and despair will cripple you.
This is Light's personality. She focuses on her goal and ignores everything else. It could be seen as the trait of a very dedicated person, it is also an outwardly productive form of escapism. By only concentrating on her present mission, she can be distracted from any helplessness she feels. It gives her the illusion of command and control. To not have a goal is to be weak again, like that 15 year old orphan she was, unsure without her mother and afraid of the future.
When her mother died, Light never gave herself time to grieve. She immediately distracted herself by creating a mission: become an adult immediately, take care of her treasured sister. Similarly, when Serah is crystallized, Lightning desperately seeks out a target. We understand why she does that by the result that occurs when she can't grasp onto a mission quickly enough. The silence screams the truth. When there is nothing to focus on, Lightning has to reflect on herself, she has to face her thoughts and fears about abandonment.
The Results
Lightning may seem arrogant at times. However, she deserves that pride within herself. She's a self made woman. Remember that Lightning doesn't come from a special background. Her family was not rich. It's very doubtful considering that it was a single parent household and that their family doctor was recommending the orphans to social services agencies. Yet she was still able to bring in enough income to afford a nice place to live, to feed her younger sister, and send her to higher education.
She wasn't special in terms of innate physical abilities either. It's her own hard work that made her the excellent fighter she is today. Lt. Amodar, her superior officer, constantly praises her, both casually with strangers, and professionally through recommendations. He points out the Blaze Edge sword to people, noting that "This is a sword given to only the best soldiers. What I'm saying is, the ones who have this sword have amazing abilities." In other words, that's Lightning, she's one of the best. She's also made it to the rank of Sergeant.
This may explain why she joined the military as well. In my country, the are mainly two types of people who join the army (There are many different types of people , but these are the general tendencies I've seen): Very patriotic kids who come from military families, or working class kids who use it to gain the money and education that their class usually does not have access to. If Cocoon's system is similar (which it may not be),I doubt Lightning is the former, but she might be the latter. People drawn to the army and the police force also often want power. Lightning might have been drawn to this profession, as opposed to more civilian professions that would also pay well, because it offered her power to protect (both herself and her family) during a time in which she felt weak and immature.