A good thing to consider when considering alignments is what some (editions) call 'contradictory' alignments. Many people can't reconcile chaotic with good, or lawful with evil.
The descriptions of these alignments give a good start to figuring them out, but unlike the other two corners people don't have a real proconceived notion of how they work fill in the blanks. And the neutral zones are even harder to place, but that's fine because it gives you a dumping ground for all characters that don't fit in a box.
Lawful evil is the easier of the two to figure out, and one with the most bearing on this discussion. Lawful evil people will follow the law, unless they can find a loophole or get away with breaking it. They do this in order to bend the rules to their advantage unfairly. They propagate the system so that they can continue to use it to oppress others. It's the downside of the rule of law, that it can oppress and entrap people, or be used to do so.
On the lawful side of the spectrum the alignment really takes more of a coherent shape than in the others. Because it factors in an external factor in the physical (game) world: the laws. Even when a LE character is doing evil, he still has a shield against repurcussion by your standard knight in LG armor: the law. It's also like a spell they can cast over any stripe of being who calls themselves a part of society. That includes warriors, wizards, armies, perhaps even magical beasts or outsiders, all manipulable by someone who has lawful influence.
From a medieval perspective, obviously mid to low level lords and such (barons, dukes, marquesses, counts, viscounts, etc.) fit this bill easily. One thing to remember: lords are not named or elected to their post. They're in charge because they own everything. This is one of the bases of feudalism. Originally, a king or emperor would take a country from another, then reward his warlords, relatives, what have you, with land, to own as their property.
Obviously, a warlord in retirement will likely come off as heavy-handed, often violently so, in enforcing his laws. Most of the time, a lord's laws don't have to be fair, just, or even logical. The king usually doesn't give it a thought as long as his tributary portion of the taxes is paid. He'll only intervene if things are made very obvious, or get very serious. This is because, once again, Lords are not appointed. They are given the land to own, and everything on it belongs to them to do with what they see fit.
This means that the state of power in the land revolves around the whims of one person, and whomever that person delegates to or can be manipulated by. There's a lot of room in there for a LE character to squeeze in, or even several. Maybe a whole infrastructure of LEs. Maybe even the Lord if people are unlucky. He doesn't necessarily have to be lawful, as long as he keeps his king happy and/or oblivious.
LE people will often use the law to hurt people, or steal, or destroy other's lives in pursuit of their own goals. If not these, they often utilize the law to protect themselves from repurcussion when they do things like it on their own initiative. Remember, the laws don't have to support justice here, simply facilitate the exercise of power by the lord's agents.
Of course LE characters don't have to be blatantly evil. They could be intractably ambitious people whose lust for power is more significant than even other LE people (which is often quite large). Or they could just have a mean streak, and enjoy handing down punishment and levying payments against others. They could even be traitors, working in secret to undermine the kingdom whilst openly working for it so they can use their authority to hide their treachery. The main point is they do so without reproach because they never break any rules (when they can get caught).
The flipside is the Chaotic Good character. These are often in response to a Lawful Evil character, if not the one at hand, often one in the character's past that influenced them. These are harder to define. Who can be good and want to do away with the rule of law?
Well in many places, even today, people live perfectly well without regulations instructing them how to live. Or at the very least, they don't bother their fellows too much. Remember, these are chaotic Good people; They wouldn't take an absense of law as a pass to murder, steal, and burn.
Most people of this stripe see regulations as an intrusion into a naturally balanced system. And sometimes it is; Ofttimes a people who mete out their own justice collectively and have a simple, efficient way of living protest the addition of new requirements of them by laws.
This all of course has the sound of a rural, poor people. How can anyone protest law in a more populous, advanced, commercial land? Such are rife with strife (that rhymes), differences, fear and greed.
Firstly, just as LE people will often break the law if they can, CG people recognize the need for some law in life. Few people of any stripe live their alignment to it's utter absolute (though they're usually paladins if they do). What such people would protest is when laws interfere with the pursuit of justice or commerce (such as LE characters rely on) rather than facilitating it. Less of control, and more of organized productivity.
Others with even more of an aversion to law find that justice and organization should be handled naturally by the people involved. If people can make laws, the people they are applied to are just as able to govern themseles. Justice is meted out in vendetta style, and public services handled by, well, the public, that is the community.
Often in a medieval setting you will find people of this bent congregating in communities outside local governance by a lord or prefect, or places hard for their agents to reach. They may also live as outlaws, forced to turn to crime to survive without accepting oppressive rule. Less commonly they could find a position within society that protects them from the affect of law. Often religious organizations can shield their members individually from law, if they have enough torque locally to stand up to local authority. Otherwise a travelling lifestyle offers a modicum of protection; At first from not being in town long enough to be noticed by the law, and then giving one the ability to escape when they do! Also, the rich can develop these traits, or gain their riches in order to escape the influence of law, as their wealth can translate into enough power to counter the law, or influence it. Though, in that case, one can just as easily find an evil being as good.
Either way, CG characters focus more on the pieces of the picture than the whole. This fits in a chaotic ideal as they wish for all things to go their own individual way. They tend to be revolutionary to some degree, even if a small one. They are often philanthropists, foregoing established means of aiding others to do so personally and in their own style. Often they can come at odds with the very people they are attempting to help; If said people are unhappy but content with the structure of things, a CG being disrupting the whole to solve the problem can earn ire, even if it was (truly or not) 'for their own good'.
Of course a chaotic character of any stripe can expect ingratitude and ire much of the time. Whether in a good or bad situation, people are often inured to the structure of their society. Besides the threat of force, people often support their societal authority structure because it keeps them safe; This is one of the duties of a Lord and their agents, and in their best interests. Such people are usually quite resistant to things that upset the status quo they've learned to make a living within.
Of course, in popular stories, LE lords often have LE lackeys whom are too cowardly and/or lazy to take up arms to do anything aside from terrorize their populace. Just another part of being evil.
Let's take the most popular example: Robin Hood. Almost universally agreed to be CG, since he was an outlaw in his own homeland (in which he was originally a landowner, part of the local authority, for bonus points).
He goes to war for a LG king (the lionheart, a RL king of england) in a far away land. This takes the usual benevolent governance of this king's lords away, and a traitor among them, prince john or nottingham himself depending on the version, works up the ambition to begin organizing a coup against him.
Obviously LE, the both of them. Especially Nottingham, as he uses his position and the command of men to perpetrate numerous crimes against the populace, on a personal level, whilst enforcing a new, corrupt decree every day. This means if John is present, he is obviously LE since his greed has completely overtaken his desire to do right by his tenants, if he had any.
Now our LG authorities reach out to Sir Locksley the senior for his pledge to join in the coup. Ill advised, since senior is obviously LG and implied to have gone to war as well, so no pushover. Unforetunately, he's outgunned by the local authority, so they murder him, then, level false charges against him (varying between versions, usually heresy). They take his land, and thus most of his power.
Then Robin of Locksley (self-titled land), breaks out of enemy prison, and for some reason, immediately deserts (already showing his chaotic side) and finds passage back home. Many stories have him without his G at this point, but after seeing his home wrecked he swears revenge, setting him firmly against the law and locking him in chaotic alignment. When faces with the plight of the people throughout the land, some forced as he is to live outside the law by their overlord, he decides to fight in their name instead of his vendetta, and shifts to CG. He continually undermines the infrastructure of the current authority structure, but because it is only helping John/Nottingham further oppress the people and not helping them much at all, they support him in his efforts. John/Nottingham react by punishing the populace, for which they cannot be challenged as they are completely in power and command a large number of men at arms. The ending of the story varies, in some without Locksley winning against his foe, but in others he eventually vanquishes the Sheriff in single combat, which finally gives him the upper hand over the whole hierarchy. King Richard often conveniently arrives close to this point and asserts the proper authority, deposing John, making Locksley lord, all the kinds of things you expect when a such a figure shows up.
This has gotten kind of long so I'll leave it at that. Give it a think
