Even if we assume that the cat was only property, such a blatant attack on another's property could be considered cause for lethal retribution in a feudal society, and Fiore is a feudal society, albeit one apparently on the verge of some sort of magic-industrialization (wasn't Lucy's father a railroad tycoon?). Remember that throughout most of human history legal justifications for homicide were easier to meet, and even under modern standards (mostly limited to self defense) Sting would at the very least go under a lesser crime.