Unlike the Lawful Good, the Lawful Neutral has no qualms about committing heinous acts to maintain order. Whether for country, for position or for the preservation of the English language, these characters believe in law above all else, giving stern chase or sacrificing their own personal feelings to achieve it.
From the easydamus character alignment page:
A lawful neutral character acts as law, tradition, or a personal code directs her. Order and organization are paramount to her. She may believe in personal order and live by a code or standard, or she may believe in order for all and favor a strong, organized government.
Interestingly, while Lawful Neutrals believe in upholding some form of law, it doesn’t always have to be the law. Characters who follow a strict personal code of honor often fall under this alignment, even if that code of honor runs contrary to the law of the land. The most extreme example of this is the Übermensch, who transcends the laws of society and becomes a law unto himself (though in a lot of cases, the Übermensch ends up being Lawful Evil).
While it may seem like most Lawful Neutrals would be antagonists, that’s not always the case. In Fullmetal Alchemist, General Olivier Armstrong may be stern and austere, but she spends most of the story on the side of the good guys. And in Girl Genius, Klaus might seem like a bad guy at first, but really, he just wants to restore order and defeat the Other. Both Death and Lord Vetinari in the Discworld series are also Lawful Neutrals, but they’re never on the bad guys’ side or the good guys’ side…they’re neutral.
In my own work, the best example of this would probably be the Patrician from Heart of the Nebula. I haven’t published this one yet, but I hope to have it out later this year. Abaqa from Stars of Blood and Glory is another good example, the son of Qasar and Sholpan. But in the works I’ve already published, Ben from Bringing Stella Home is probably the most prominent Lawful Neutral.