Can't say as I've ever drawn one up in detail but I have considered them. Especially Lawful Evil. I would say that a LawfuL Evil country would not necessarily be a bad place to live. Stable society, clean streets, trains that run on time. Obviously there'd be a secret police force or two and everyone would fear the early morning knock on the door and being "disappeared." But small prices to pay for a reliable train timetable.
I think the thing to remember is that the society is LAWFUL as well as evil. There will be those folks who will place as much or more emphasis on the Law as on the Evil. Folks to whom the Law is important at the most visceral of levels. I can't help but feel there would be an emphasis on the form over the spirit of any laws. Not to mention a certain amount of "if you can get away with it, then it's OK." But law nonetheless. Values that would be held dear would be stability, tradition, the group as a whole rather than individuals within it. In fact I'd say that the needs of individuals being made wholly subservient to the society would be a hallmark. Justice without mercy.
I think Gilladian has a good point. There will be a greater percentage of evil people closer to the power centres. After all, one of the things that is used to define most evil characters is a desire for power. But also the constant struggle for power within the higher echelons would lead to a winnowing out of the unfit (read: those who just don't play hard enough.) Something that the society as a whole might well approve off as it means that the leaders are the ones best qualified to kick ass in the dog-eat-dog daily struggle that is the world. A negative world view like this would be an essential part of the underlying philosophy. A Lawful Evil society believes the world is tough, unforgiving, morally bankrupt and actively hostile, so the society needs to be as well in order to compete. The most important skills in a such a government would be Bluff, Sense Motive, KS: Bureaucratics, Uncanny Dodge and Paranoia.
Something a lawful evil society must have is laws. If you're drawing one up I'd suggest coming up with a list of laws for it. This will let you know what the society deems appropriate behaviour. Or even necessary behaviour. Obviously cover the biggies: murder, treason, theft, being a member of a proscribed group. But also little ones like attending church, obeying the social pecking order, sumptuary laws, maybe even the times to eat and sleep (ala the military and prison.) As well as purely arbitrary laws that serve no purpose save to be laws, like in Kafka's
The Trial. And consider the official exceptions to the rules. As the Clash sing: Murder is a crime, unless it's done by a policeman.
On the surface I don't think you'd see much difference between a Lawful Good society and a Lawful Evil one. The time it would be most obvious would be when the society deals with someone who breaks the Law. If you're a thief you'd much rather be in the charge of a kindly, naive social worker than a concentration camp guard. There'd also be an air of paranoia and distrust to a LE society but this may not be immediately noticeable.
For inspiration look to Nazi Germany (Ya know, taken out of context that would sound SOOOOOOOOOO bad) or any modern communist dictatorship. As I mentioned above
The Trial by Franz Kafka is another inspirational read. ANd, although it's on the lighter side of tryannical despotism, the old Paranoia game if you can find a copy.
I've harped on about the Law side of things, but I think most people already have an idea of evil in the DnD sense.