IC Inbox (Holly Heights)
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And, like any good ruler, she'd do anything to save her people. While she was born to two loving parents in a prosperous kingdom, both of her parents were killed in the onset of a major war that devastated their kingdom, leaving her and her sibling orphans. Growing up in a warzone certainly left a mark on her personality. She became resourceful and determined, if only because anything else meant death. When one of the gemstones that's necessary to drive the fell dragon Grima from their land is lost, she spearheads the effort to go back into the past to defeat him before the calamity can occur. She constantly strives to do anything she can to prevent the terrible future from occurring, from thwarting an assassination attempt on the exalt, to almost killing Robin (the future vessel of Grima), despite the former being her father's best friend.
To achieve her goals, she's even willing to sacrifice her personal happiness; when she first ventures into the past, despite meeting her father and extended family, she doesn't reveal who she is, instead working alone from the shadows. In a conversation at the hot springs with Robin, it's revealed that after the war is over, she's planning to disappear from her parent's lives because she's afraid that her presence will cause them undo hardship and worry; her epilogue reinforces this, and it's revealed the last thing she says to her current self is that "[hers] will be a happy future."
Despite Lucina's strong exterior, however, she's a very emotional character. When she first reveals who she is to her family, she sinks into her father's arms, crying, after finally being reunited with her family after so long. Although she doesn't admit it, her experience in the future fills her with a constant fear and dread that the past cannot be changed. She admits as much in her non-sibling conversations with Morgan; she's afraid, despite their efforts, Grima will be resurrected. She also shows this fear in the Future Past DLC; when the company is taken to a future similar to her own, she insists that her father not fight, afraid that she'll lose him again.
And her father, Chrom, is certainly the most important person in her life. Although it's never mentioned how old she was when he died, she was old enough to have been taught swordplay, and at least have been partially raised, by him. It's his death that sparks the war, and it's him that (in addition to her country), that she travels back in time to save. In her non-parent support conversations with Robin, she goes so far as to track Robin's movement outside of her father's tent, afraid that their strategist might have "nefarious reasons" for being nearby. Even though it's occasionally played for laughs, Lucina loves her father more than anything, and carries Falchion constantly at her side, wanting more than anything to follow in his footsteps.
Although not as strong, she has a good relationship with the rest of her family, too. In her sibling supports, it's revealed that the same serious attitude that she had in the future seems to be the same attitude she has in the present, that gives off an air of being unreachable. She can also sometimes grow frustrated with her sibling, or show a less serious side of her personality, even if it is rare.In her mother supports, she goes shopping with her mother, even if her mother later ends up regretting it, as it's revealed that Lucina has a horrible fashion sense.
Her horrible fashion sense is an offshoot of her difficulty reading people, which was likely caused by the conditions which she grew up in. She reveals in her supports with Noire, that she wasn't initially able to tell when the former was angry or upset, and only realized it after Noire herself had pointed it out. In her supports with Robin, Robin refers to her as someone who "holds nothing back" and "says what's on her mind, no matter what." Her bio describes her as the least likely to understand a joke in the army.
However, even though she has a difficulty reading emotion (such as in a joke), it doesn't negatively affect her relationship with her comrades. She's a (painfully) honest and hardworking person, which tends to naturally draw people towards her. Her support conversations with Tiki point this out; when she has free time, she goes around and helps the army with its chores, for no other reason than she has the time to do so. Everything she does she does with enthusiasm and the best intentions (even if it sometimes it goes awry, ala Robin's support conversations or Tiki's Harvest Scramble conversations), and people rarely fault her for it. She's a natural leader, who often doesn't realize the effect that she has on people, and is every bit the image of the old hero-king, Marth.