A lawful neutral character is directed by law, logic, tradition, or a personal code. Order and organization are paramount to him. He may believe in personal order and live by a code or standard, or he may believe in order for all and favor a strong, organized government. In 4th edition mechanics for Dungeons & Dragons lawful neutral is found under the umbrella of the "unaligned" alignment.
Lawful neutral combines reliability and honor without moral bias. Note that this does not mean that a lawful neutral character is amoral or immoral, or does not have a moral compass, but that moral considerations--the good or evil of the action--come a distant second to what the character's code, tradition, law, or logic dictate.
Jean-Luc Picard is a good example of Lawful Neutral