I'm going to wait until you write something. I'm sick of dealing with this guy, and fem-Spock waifu.
Okay, let me come up with a quick list
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<> She is one of 8 characters who get two whole new marrage specfic conversations during the Scramble DLC, so more content there if you pair up with her over others.
<> Gameplay: She is arguably one of the most powerful 2ed generation characters, with only Morgan and the Robin-fathered versions of the other 2ed gens being stronger (and her Robin-mothered version is just as strong as the later)
<> Her personality: Lucina is one of the more psychologically complex characters, being simultaneously very grown up and childlike at the same time. She grew up in a hellish apocalypse world starting when she was only around 10 years old, forcing her to grown up very quickly. She has gone through more than most people during her teens than most others have: making her incredibly driven, serious, and willing to make hard choices. Yet at the same time she is still very childlike in how she interacts with others, almost certainly from having her childhood cut short. She gets embarrassed easily, and over all doesn't really know how to interact socially as an adult. You can see this in her supports with her parents and her siblings. It has this interesting duality of her being simultaneously one of the most serious and grownup-like characters, while also have a side that still at heart someone who never had the chance to finish her childhood.
In addition, she managed to be both a very strong character, while also being vulnerable at the same time, adding some more complexity. Rather than list all of the examples, I will focus on one moment, the cutscene in chapter 13. Imagine what Lucina must have been going through up to that point. Coming to the past, having a chance to see her parents alive again after what was for her years of them being dead, yet being unable to say who she was. Having to spend two years alone, keeping her distance, probably watching over her family from afar. Two years alone, not know what happened to friends, not know if they were even alive or dead, having last seen them entering the portal leading to the past only for them to not emerge on the other side with her.
Then, after all of that, when she finally reveals who she is to her father, the first thing Chrom does is apologies to her for everything that happened to her, having realized that she comes from a future where he failed his daughter, where he left her "with nothing more than a sword and a world of troubles". Its no wonder she broke down then, letting everything she'd bottled up for years out at that very moment.
<> Her (potential) relationship with M!Robin: This is probably one of the most deep relationships in the game, in no small part due to the extra content it gets, that also adds to the main story. This is expressed through the Hotspring conversation they have, as well as the unique version of the Judgment scene in chapter 21. In this conversation it is revealed that one of Lucina's greatest fears at this point is of having to be forced to pick between Robin and her mission to save the world. She says that if that were to happen, she would have to choose the mission, since its too important, and feeling guilty that she can't put Robin above all else as she should. Well, chapter 21 rolls around and Lucina is faced with that very choice. She can kill Robin there, and in her mind stop what happens in her timeline. This is where the unique version rolls in, as even with Robin telling her to do it, even with Chrom not yet stepping in to stop her, Lucina realises that she can't do it, that she can't kill the man she loves, even if logic and her duty say otherwise. She is faced with the choice she feared, and comes to a different conclusion, that for all that the parallel Robin did, she cannot bring herself to harm the man she loves.
Finally the hotspring scene reveals something shocking about their relationship... the true extent that Lucina cares about Robin. At the end of the conversation, after he leaves, she reveals (speaking to herself) that Robin is the dearest thing to her in the world, and that she would consider herself the luckiest woman alive if she were to have a chance to grow old with him (something she was afraid wouldn't happen, since she thinks she will need to return to her own timeline). Furthermore she reveals that Robin and the future she wants with him has become her biggest motivation to the save the world. That's right, her other motivation of stopping her parents death and creating a world where others can grow up free of the horrible future she lived and that her younger self can have the childhood she was deprived, all of those are not her main motivation. She cares for Robin more than all of that. It is shown here that despite her fears and her misison, she truely loves him above all else.
Also there is the fact that Robin promises her and not other possible spouse that he will support her for the rest of his life, no matter what happens. That if she decides to go back to her own time, he would leave everyone to get with her. That even if he died, he would find a way to come back to life, just for her... which if you sacrifice yourself at the end, the epilogue shows that he keeps this promise. All of the touchingness and feels right there.