Relationships: Hope Estheim
"Fighting without hope is no way to live. It's just a way to die.
I want you to find the hope you were named for."
When Lightning opened up to Hope first, it was extremely surprising. Surprising because she had been so cold to everyone else up to that point. Sazh, Snow, Vanille all tried to work with her and were abandoned by her either at Lake Bresha or the Vile Peaks. Hope was persistent though. And the person who ended up breaking Lightning's icy wall first was none other than the weakest, smallest, youngest cast member.
Sibling Surrogate
After fighting Odin together at the Vile Peaks, Lightning agrees to allow Hope to tag along, and to teach him how to fight. Their relationship develops immensely in the Gapra Whitewoods and Hope's hometown of Palumpolum. The act of Lightning giving Hope her survival knife is symbolic. That knife was given to Lightning as a gift from Serah, and it represents how the role of "younger sibling" becomes passed down from Serah to Hope in Light's eyes.
Lightning: "Can you handle it?"
Hope: "It's not a question of can or can't."
Lightning: "Now you're learning."
He fills a void in Lightning's life. Hope needs Lightning, in terms of survival and advice, something Serah no longer needs (as she has matured into a strong person and is now engaged to Snow). Despite what she said about wanting to leave him behind, Lightning wants to be needed. She has defined herself as a protector and provider for Serah for her entire life, so she leans on Hope to hold onto that purpose. Indeed, Hope reminds her of Serah, as when Hope talks about his past, it triggers memories within Lightning of the birthday argument with Serah.
Future lover
Yes, Hope is 14 in the story, while Lightning is 21. I don't like shota, and the thought of a 21 year old dating a 14 year old is disgusting. However, Hope will not always be a 14 year old boy. By the time he becomes an adult, that 7 year age gap is going to be less important, especially since he has the ability to mature quickly, as shown in the game. What started out as a platonic relationship of emotional support could easily become a romantic relationship in the future.
Hope: "But--you can't do this. You can't just build something up like that, then abandon me."
Lightning: "I won't abandon you. I won't."
Hope is going to grow up to be a strong, mature man (and probably a bishounen). This evidenced by his eidolon, the holy fortress Alexander, which represents the strength within him. Furthermore, even as a kid, he's able to hold his own and be a valuable member of the l'cie. Lightning is a tough person to connect with, yet Hope was able to build an intimacy between them in short amount of time. She has referred to him as her partner and thinks that they are similar (in the grief felt after losing their parents). The trust they have for one another makes for a good foundation for a relationship, and it is likely this trust will continue to grow as they both will keep in contact as they continue maturing individually.
In Hope's Eyes
So far, we've mostly covered what Hope is and could be to Lightning. But how does Hope see Lightning? Let's look at his situation. He's young and impressionable. 14 years old is a difficult age in a person's life because they are transitioning from childhood to pre-adulthood. You are expected to as as maturely as an adult, but clearly do not all the resources and wisdom from past experiences as adults do. To make it worst, Hope just lost his mother and a sense of normalcy.
Lightning: (Regarding the Alexander battle)
"This is not an ordeal, this a gift! Hope, this the kind of power you got inside.
And it's telling you not to give up. Trust me."
For Hope, Lightning is a perfect pillar of strength to nurture and support him through this transition. She comforts him like a child, when he needs it, like during their first days on Gran Pulse. At the same time, she advises him on how to grow as a person, such as when she lets him take point in the Gapra Whitewoods, and teaches him battle strategies. She's a role model who is not unreachable. With Light's help, Hope grows wiser, in many ways, through the game. Judging by how Serah turned out, Lightning definitely knows to raise youngsters well.