Lightning doesn't know why people compare Fang to fire.
Sure the Pulsian is loud, brash, and infuriatingly annoying, but she's anything but full of fire. Some call her flirtatious, as she wears her sexuality as easily as she wears that sari. But Lightning isn't blind, and she isn't stupid. The soldier can see through the façade as easily as Fang dispatches Pulsian beasts.
Lightning can read Fang in a way unknown to the others in their ragtag band of l'Cie, she can see past Fang's loud and annoying exterior, and into who the huntress really is. Fang is capable of lying with her mouth and her body, but she can't lie with her eyes. The soldier finds it bitterly ironic that the huntress' little sister cannot see the conflict and internal pain Fang is suffering through, whereas Fang can see Vanille's and offer temporary solace from the cruel reality of their fates. Vanille at this moment is too far gone; wrapped in her own little cocoon of problems and choosing ignorance over choosing to face the reality of what her older sister was feeling. She may be able to lie with her mouth and body to the rest of them, but her eyes don't lie to Lightning.
She sees it all within Fang's eyes, the loss and pain.
In fact, Fang is in so much pain that she's frozen with it. Inside of her is a desolate icy wasteland where nothing could survive, a place so cold and so shut down from the world that Lightning doubted even with her limited interpersonal skills she could reboot. Light reflected for a moment, she'd seen people like Fang before in the Corps. Soldiers who were shell-shocked to the point of complete shutdown from the world, they retreated and tried to escape the world emotionally. She finds herself surprised Fang is still functioning and is still able to get up in the morning; functioning the way she does. Perhaps she was saved by her memory loss, she has no memories of the happenings in her world so she doesn't need to live with the memories of what she did to her homeland, but she must live with the consequences instead. It was much better than a constant reminder in the soldier's opinion.
Lightning seems to understand the burdens that Fang carries as she carries a similar one. How it must have felt to carry the hopes, dreams, and well-being of an entire civilization only to fail at the last moment where it counted the most. She had an impossible mark to measure up to; and when she failed, she lost the memory of her failure but now faced the consequences.
It's not fair to Fang – everything she's doing; they're doing seems to be playing right into the hands of the Fal'Cie. But it's not Fang's fault, and it's a revelation she'll have to come to when everything isn't locked down tight and sealed with frost. Lightning isn't the best with emotions, even she'll admit to that, but she wants to help. Wants Fang to see that this isn't her fault, wants her to toss that easy smile and really and truly feel it.
Lightning wants Fang to look in the mirror and see the woman she sees.
Lightning knows Fang can get there; she's sure of it. Because Lightning likes Fang, likes her in a way that makes her face flush and her heart beat faster, and gives her butterflies low in her stomach. She wants – hopes that she can make Fang feel the same way but before that, Fang has to thaw.
And then, only then when Fang can feel, Lightning may be able to show Fang how she feels. Show Fang what she does to her; take her hand, press it to her chest and show Fang how her heart races. Then, carefully, gently press Fang back into the grass and show Fang what she means to her.
As Lightning sits at the small campfire at night she looks across to Fang silhouetted against the silvery blue backdrop of the crystal shell of Cocoon. All she can do for now is sit there and wonder;
"What can I do to break the ice?"