A weird PF character concept I got yesterday...
I generally do agree with the "murder hobo" description of player characters in general, so a character who 'just travels around killing people gruesomely' doesn't actually strike me as all that different from the average Paladin. It just depends on who you consider `people'.
Now, games focused on evil PCs crop up periodically - so there's clearly a place for them, and it sounds like he'd fit right in there. If you're curious about how a character like that could work in a more traditional campaign - well, Lawful Evil tends to play better with others than any other kind of Evil. One of my more carefully thought-out concepts was a Cleric of Incabulos in a Temple of Elemental Evil campaign -- she never pretended to be anything she wasn't, but she understood that she was, you know, outnumbered, and the one who asked to work with them. So she absolutely had her Evil perspective on things, but she was a good team player.
Reading some of the wikis on Kyton... yeah, I can see a couple of ways they could work. Being Lawful, they might just agree that they're subject to the Laws of whatever kingdom they call home - laws that probably prohibit murdering `people', but which probably have big loopholes for races they consider `monsters', or people who have shown themselves to be `bandits', or... whatever. Or maybe they just find it interesting to find the ways to sate their needs within that structure. Or maybe they've worked out that a group of adventurers is the best way to find and defeat the kinds of stronger creatures they want to replace bits of themselves with -- even if it means ignoring lesser opportunities along the way.