I haven't played tabletop Dungeons and Dragons, but I've probably sunk like a hundred hours into Baldur's Gate, so I'm sorta familiar with it. That said, I think the DnD alignment system is inherently flawed and suggest you don't worry too much if the alignments don't quite match what the books say they're supposed to be.
Anyway, Lawful Neutral is typically for Inspector Javert style characters, but I think anyone who feels like a robot in a cast of humans would work. A calm, polite and professional mercenary/assassin/whatever who would never ever break a contract a finds the very thought completely alien. A ruthlessly efficient ruler who sees his subjects as statistics rather than people, but feels obligated to guarantee their well-being nonetheless. An actual robot, ie. some kind of intelligent construct, who's spent the last several centuries trying to complete a fetch quest for his long-dead master. Or
Inspector Javert, of course. Someone who's going to chase the party to the edge of the world for an unpaid traffic violation and would rather die than let them get away, no matter how justified it would be.
Chaotic Evil seems pretty straightforward to me. A schizophrenic who wants to kill the party because the Voices told him to. A paranoid who wants to kill the party because he thinks the they are in league with the Mind Flayers. A monomaniac who wants to kill the party so he can have their teeth. A sociopathic adventurer who wants to kill the party for experience. Just have a guy who wants to kill the protagonists for some arbitrary reason that doesn't really make sense, and does not necessarily involve any kind of obvious benefit for the killer.
Or you could take the Planescape: Torment approach, and make True Neutral the "batshit insane" alignment, reserving Chaotic Evil for people who are purposefully and and selflessly trying to further the cause of Evil. Maybe a cultist who worships an evil deity/fiend/Great Old One, or perhaps just a freelance puppy-kicker who has dedicated his life to the pursuit of evil and feels compelled to do evil regardless of its utility. Hey, it works for good-aligned characters.
In this case, flat Neutral would be anyone who doesn't think about the consequences of his actions enough to have an alignment. Lunatics, soulless automations and generally people who are incapable of thinking that the act of attacking the party could have some kind of moral ramifications.