A LE character can be a Kantian Deontologist who just goes against his moral code while obeying laws that are enforced by others. Or a Consequentialist who holds to his moral philosophy regardless of the people harmed along the way. Or he can adhere to Subjective Morality. Or Nihilism. Or be an Existentialist who doesn't care who he hurts because they'll just go to D&D heaven, anyway, so who cares whether they die now or 30 years from now?
Here is Gygax on Lawful Evil (PHB p 33; DMG p 23):
Creatures of this alignment are great respecters of laws and strict order, but life, beauty, truth, freedom and the like are held as valueless, or at least scorned. By adhering to stringent discipline, those of lawful evil alignment hope to impose their yoke upon the world.
Lawful evil creatures consider order as the means by which each group is properly placed in the cosmos, from lowest to highest, strongest first, weakest last. Good is seen as an excuse to promote the mediocrity of the whole and suppress the better and more capable, while lawful evilness allows each group to structure itself and fix its place as compared to others, serving the stronger but being served by the weaker.
We can elaborate on the second paragraph by inserting, as the subject of its second sentence, what Gygax means by
good (DMG p 23):
the tenets of good are human rights, or in the case of ADBD, creature rights. Each creature is entitled to life, relative freedom, and the prospect of happiness. Cruelty and suffering are undesirable.
Putting it all together, we get:
Lawful evil creatures respect law and strict order, as a means by which each group is properly placed in the cosmos, from lowest to highest, strongest first, weakest last. Life, beauty, truth, freedom and the like are held as valueless, or at least scorned; human/creature rights, life, freedom (including freedom from cruelty and suffering), and the general prospect of happiness, are seen as an excuse to promote the mediocrity of the whole and suppress the better and more capable. By adhering to stringent discipline, those of lawful evil alignment hope to impose their yoke upon the world, with each group structuring itself and fixing its place as compared to others, serving the stronger but being served by the weaker.
This position is not compatible with any standard form of consequentialism, which (depending on details) places a great deal of value on life, freedom from suffering and the prospect of happiness and does not see these simply as an excuse to promote the mediocrity of the whole.
Nor is the position compatible with Kantianism or existentialism. It is radically at odds with the notion that each person is an end in him-/herself; and is at odds with the notion that each person is a unique site of value/goal creation.
It could be a form of nihilism. Or just an immoral person who enjoys being part of a group of like-minded bullies.
. (Chaotic evil in certain countries, though....)
