Lawful Neutral is called the "Judge" or "Disciplined" alignment. A Lawful Neutral character typically believes strongly in Lawful concepts such as honor, order, rules and tradition, and often follows a personal code. A Lawful Neutral society would typically enforce strict laws to maintain social order, and place a high value on traditions and historical precedent. Examples of Lawful Neutral characters might include a soldier who always follows orders, a judge or enforcer that adheres mercilessly to the word of the law, and a disciplined monk. Characters of this alignment are neutral with no affiliation to good nor evil.
This does not mean that Lawful Neutral characters are amoral or immoral, or do not have a moral compass, but simply that their moral considerations come a distant second to what their code, tradition, or law dictates. They typically have a strong ethical code, but it is primarily guided by their system of belief, not by a commitment to good or evil. Nevertheless, these characters are considered successful like Neutral Good characters are. This is because they enforce and employ fair and rules and laws to maintain order, and protect their beloved society at all costs, but not for either said side.
Pure Good heroes NEVER fall under this alignment. The type of Pure Good hero that falls under the lawful character alignment always falls under Lawful Good.