Yeah, thats confession scene where Lucina admits who she is, probably one of the most touching scenes in the game. There are only two moments I like more, both of which are Robin x Lucina specific moments (one in the main game, one in a DLC). Though that confession probably has the single best line in the entire game: "You deserved better from me than just one sword and a world of troubles".
You really have to think just what Lucina went through since the appeared at the start of the game up to where she revealed who she was. Getting to see her parents again, alive, but without them recognizing her. Having to spend two years keeping her distance, not being able to tell them who she is. Two years of being alone, not knowing what happened to her friends, since they went into the portal with her but didn't come out on the other side (since the rest of them ended up at different places and different points at time, some even years before or after she arrived). And the entire time she managed to keep all that in, to do what she had to. So when she finally revealed who she was its not wonder she let everything out at that one moment. Not to mention that she really needed that hug.
One of the advantages of pairing Lucina with Robin is that it leads to character growth that otherwise does not happen in the game, which I won't spoil for you. This can be found if you ever see the romance specific conversations she had with Robin in the Hotspring Scramble DLC map, followed by another scene in chapter 21 (both of which are the two best scenes I mentioned before). I say in that order since the conversation in the DLC actually forshadows the chapter 21 scene a bit, and makes the outcome even more meaningful. Just when you get to that scene make sure to have Robin select "yes". since while it doesn't really change the outcome, the dialogue is better in that version than if you say "no". Sorry if I am being vague, since I do not wish to spoil it.
And yes, Morgan is completely adorable.
Side note: I am slightly miffed that Lucina's Final Smash has her say "Time to change fate" rather than the proper quote of "I challenge my fate!"