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.
A functionary, soldier, or employee who follows orders without question regardless of the result, an arms dealer who sells his wares to the highest bidder, whatever that bidder may do with them, and an impartial jurist who sticks rigidly to the rule book are all examples of lawful neutral characters.