Symbolism.

A common sight seen within Fire Emblem: Awakening is the image of a butterfly. This butterfly can be seen multiple times during the opening movie, and is also the shape of the mask Lucina uses to hide her Brand. It is also seen on her shield in her Great Lord class. There is even official artwork of her with butterflies within it, plus her name comes from various moth and butterfly species names––the Dactyloceras Lucina, the Hypatopa Lucina, and the Hamearis Lucina. Obviously butterflies play some part in Lucina's character, but is there any hidden meaning to all this? I seem to think so, so I've gone and done some digging.

Butterflies can represent a variety of different things depending on what context they are used in. As such they can have a variety of different meanings. In terms of symbolism, however, butterflies can represent time, soul, grace, growth, lightness, expression, resurrection, and vulnerability. The most common form of symbolism of a butterfly––and perhaps the most relevant to Lucina––is transformation. A butterfly goes through multiple changes throughout its lifespan, from egg to caterpillar to pupa to butterfly; this transformation can be seen as steps taken on a journey which can translate over to Lucina's journey as well as she travels to the past in order to change the future, all the while changing herself in the process.

These changes can also be seen as a sign of faith; to trust the changes that will happen and to embrace it with everything one has. When Lucina decided to travel back to the past she had to leave behind everything she knew and all that was familiar to her and go to a place completely new, not entirely knowing what to expect, but trusting everything will be fine. Although her intentions aren't exactly embracing change, as she is trying to change events to prevent them from happening, she does go through her own sort of transformation after she joins Chrom and company, especially when she discovers it was Robin who had killed her father. When she confronts them in order to kill them, she is stopped by Chrom where he then says these words to her:

Lucina, aren't our ties stronger here now than they were in your future? You said so yourself. In this flow of time we are bound tighter than ever, you and I. Not just as father and daughter... But as friends. We can change things––we already have...and we will again.
– Chapter 21: Five Gemstones

Although Lucina is convinced that if she does not kill Robin her dark future will come to pass, Chrom is able to convince her otherwise; that their bonds are strong and therefore they will not fail. Lucina could have just as easily argued with him that it was impossible, but instead she takes a leap of faith and trusts in what he is telling her. I think if she had not revealed herself to Chrom and stayed by his side all this time it would have turned out very differently and perhaps she would not even hesitate to kill Robin, so to me I see this as a sign of transformation; the caterpillar has become the butterfly.