At the moment, there's not much in the way of a story, but the way things are going now, it looks like there might be a story in the next release.

There is a castle of some sort, with enemies; I've planned out the areas in advance (though some areas might not make it in the current release).
With a name like Lunar Shadow, it might have to do with the moon. Or shadows. Or souls, considering the castle's name is "Lunar Soul".