Lawful neutral is one of the nine alignments in Advanced Dungeons and Dragons. The game's 3rd edition Players Handbook calls the lawful neutral character a "judge." His worldview values order and stability above all else.
The lawful half of the alignment refers to the character's disposition towards law and chaos. Law, tradition, stricture, or creed are paramount to her. Indifferent to moral hair-splitting regarding good and evil, she believes that obedience to established truths or codes of conduct suffice to keep the universe, or at least herself, in balance.
The neutral half of the alignment refers to the character's attitude towards questions of good and evil. The temptations of evil and the duties of good do not sway him one way or the other. They are unimportant distinctions. Since AD&D defines good and evil along the lines of how one values life and the common good, the lawful neutral character may be indifferent to what the consequences are for others resulting from his disciplined, structured life. Or perhaps, he believes that observance of law takes care of everything and that disobedience is the only evil.
Thus the combination of these two elements -- law plus indifference towards good and evil -- produces a character that may act bureaucratic or cold. He will obsess over tradition, procedure, or process rather than results and consequences. You might think of Martin Luther King Jr.'s admonition to the white moderates, that they are "more devoted to 'order' than to justice." Monks make good lawful neutral characters since they lead highly disciplined lives, removed from the day to day cares that bring up discussions of good and evil.