n., adj., in Dungeons & Dragons, the alignment of a character that serves the forces of law, but also evil. See also lawful good, neutral good, chaotic good, lawful neutral, true neutral, chaotic neutral, neutral evil, chaotic evil.
Addendum: Lawful evil is the alignment of real-world hedge fund managers, televangelists, and some sociopaths. This person adheres to the law, and even to codes of religious conduct and social propriety — but these laws are a system to be exploited, not a system to serve others. The goal of the lawful evil character is self-aggrandizement and personal power (or, in a fantasy milieu, to serve evil or corrupt powers for the purposes of self-aggrandizement and personal power); and this person will use the power that comes from government, bureaucracy, organized religion, the military, or any other established hierarchy to get it. They willingly serve the hierarchy, but their motivations are purely evil.
There is a second take on the lawful evil character, which applies to examples such as Darth Vader and the Empire in Star Wars, or to Fascists and Communists in real life. In this take, the character genuinely believes that law, order, and peace are paramount above all other considerations; and he or she is willing to perform any sort of monstrous action if they believe it will promote those goals. One can argue, however, that this is actually closer to lawful neutral.