As stated before, "lawful" is exactly how it sounds. Your lawful character will stay within a set of rules; whether it is society's rules, a smaller community, or their own personal code. Whether they truly believe in the system, or are coerced by fear, lawful characters will not break rules, no matter their moral alignment.
Below I will discuss the different alignments on the lawful axis. I will describe the alignment, give examples, and some conflicts that those characters will find difficult to deal with.
Remember, your character's alignment will determine their actions and reactions. The conflicts you provide them will either keep them firmly established in their alignment, or will force them out.
If you are wanting your lawful character to switch alignments, please see the "best practices" post.
LG characters are rule followers. It isn't just the fear of getting in trouble (which can be a great motivator), most of them truly believe in the system they are a part of. They are generally a paragon of society, trying to emulate how they think everyone should behave. Think of the heroes we idolize. With the exception of the vigilante types, most of our heroes uphold society's laws, even though they are powerful enough that they could force their views on others. LG characters believe that to be good, you have to follow society's rules, OR that if you follow those rules, you are automatically good. It may seem like that's the same thing, but there is a distinction.
These characters are altruistic, however, they tend to think in "big picture". They may help a homeless person on the street, but not because they want to help the individual. They will help because they are "bettering" society. They believe so strongly in the system they are a part of, that they may put aside their personal feelings on a subject, simply because they trust the system.
This belief is ingrained into their character. If they see something wrong with society, or feel something is unjust, they will work within the confines of the system to fix it. This may include trying to get laws changed, or finding alternate ways to solve a problem, without breaking the law.
Some examples of a LG character are:
-Ned Stark (Game of Thrones)
-Choal Westfall (Throne of Glass)
Unlike the LG alignment, LN characters aren't as concerned with morality. They understand the world isn't black and white, but shades of grey. They understand that sometimes you may have to do the wrong thing, for the right reason or doing what is right, for the wrong reasons. They don't try to label themselves.
They do however follow the rules. This is could be society as a whole, or their own personal code. There are a lot of excellent examples of this, for instance, Judge Dredd. He upholds the laws of his society while enforcing it on others. He is authorized deadly force, and has no issue killing people in the name of the law. However, he doesn't kill anyone unless required by the law. Killing doesn't bother him (even though murder is a crime), because he is only killing in the role of Judge.
Other LN examples (from my point of view):
-Frank Castle (The Punisher)
- Dexter Morgan (Dexter)
By now you understand that "lawful" characters follow the rules. But when we think about "evil" we tend to think of rule breakers, or those that go against society's laws. But there are many instances when evil is structured, with rules, that must be followed. Even those at the top will follow the rules. If they find themselves in a position where the rules are hindering them, they may work to get the rules changed to accommodate their desires.
LE characters are evil, but they commit evil acts from within the structure of a system. The best example I can give is demons. We have heard about levels of Hell, different parts of the underworld. Each of these levels have different torments, and different demons to torment souls. But think about who is in control of those demons. Throughout literature, we see a hierarchy. The powerful control the weak, with one supreme demon/devil reigning over them all. It is their rules the demons follow, knowing that if they break those rules, they will be punished.
Organized crime operates the same. There is a system of accountability, and a way to enforce rules. Fear is a tool that is used to control others.
One of the main traits of a LE is that they are forcing their system onto others. This can be done through violence (or threat of), blackmail, extortion, or simply changing the laws to suit their own purposes. They want the world to follow their rules, and will do whatever is necessary to make that happen.
Some Examples of LE characters:
-Tywin Lannister (Game of Thrones)
-Delores Umbridge (Harry Potter)
Some conflicts you can give these characters:
-Present them with a choice to either break the law/ personal code or allow something to happen that goes against their good/evil alignment
-Have the system fail/betray them. Disillusionment in the system causes a lot of internal conflict
-Doing what is morally right vs. doing what is legally right
-What if they are not able to solve their problem within the confines of the law/code? Are they willing to step outside of the rules in order to accomplish their goals?
-What could make a good character evil or vice versa?
-What event would have to happen for them to fight AGAINST the system?