One common theme is adventure. Since both characters are from the Fire Emblem world which is full of battles and quests, many fanfics might center around them going on adventures together. Another theme could be love and relationship development. Writers often explore how their relationship grows from initial acquaintance to something deeper.
Many 'lucina x robin fanfic' explore the theme of self - discovery. Lucina and Robin are complex characters, and through their relationship in the fanfics, they might discover new aspects of themselves. The theme of trust is also common. As they face various challenges together, they need to build trust in each other, and this forms an important part of the story in a lot of fanfics. For example, in some fanfics, Robin might be initially distrusted by Lucina due to his or her unknown origins, but as the story progresses, they learn to trust each other completely.
A prevalent theme is the struggle against destiny. In the game, both Lucina and Robin have their own fates and destinies to deal with. Fanfic authors like to play with this idea, showing how their relationship either helps or hinders them in facing their destinies. Also, the theme of sacrifice is often present. Given the nature of the game, characters sometimes have to make sacrifices, and this can be a big part of their relationship in fanfics.