ThrorII
Adventurer
Interesting.
I've always seen "lawful" as implying one follows external laws e.g. those of a kingdom or temple or whatever, where "chaotic" either follows one's own internal, personal laws or no laws at all.
Easy. An LE person either uses/twists laws to evil ends, or willingly follows and supports (or willingly helps enforce) evil laws, or (if in power) writes evil laws and puts a strict enforcement mechanism in place. That sort of thing.
Lawful Evil could be seen as Star Wars' Empire, or the Roman Empire.
It is structured, it has clear laws and ordered society. But it is also cruel and direct:
"We crucify criminals"
"The penalty for unpaid debts is slavery"
etc.