Lawful Evil Alignment

For a Lawful Evil character, ‘lawful’ does not necessarily mean legal rules, but it can be. Lawful Evil characters are often outlaws but they follow their own code perhaps by joining with others in a guild or gang. Corrupt government members are likely to be Lawful Evil.
A Lawful Evil character views themselves as above other unruly criminals. They are part of an ordered system with codes, honor and often strict hierarchies. They carry out selfish acts but they do it according to a carefully constructed set of rules and oaths. For a Lawful Evil character, following these codes and keeping their promises is just as important as it is to a Lawful Good character.
The codes they follow might prevent them from harming or eliminating residents of their town, but they can take out anyone else. They are unlikely to do it out of enjoyment (though some Lawful Evil might), they are more likely to do it because they are ordered to and they will gain reputation or other rewards for it. They use violence as a tool that they must be careful with.
Hierarchy is important to a Lawful Evil character. It is how the strongest rise to the top to lead everyone else. It means that the weakest people are at the bottom of the hierarchy which is where they deserve to be. If they want to rise up, they need to be stronger and prove themselves. That is the only fair way to decide.
A Lawful Evil character will respect and follow those above them. However, they would usually like to be promoted within their order and lead others. They may follow the system because they can use their role within it to control others. They will use the rules of the system to their advantage whenever possible in order to rise in the ranks and to gain power. The Lawful Evil leader better watch their back though. If at any time they are perceived as weak by their followers, or they start acting out of line with the codes, their followers will deem them unworthy to lead and will displace them and promote a new, more powerful leader that follows the code.
Lawful Evil characters are likely seen by those outside of their order as evil, but the Lawful Evil character might not perceive themselves that way. They might think they are doing what is right for society and the world. To them, they could be bringing peace to the kingdom, or using strict control measures to keep everyone in their place so that society works as it should.
Some Lawful Evil characters might be aware that what they are doing is evil, but they hide behind their codes and laws to justify their actions. As they progress through the ranks of their order, they may get lower status members to do the most evil acts for them, to further distance themselves from evil and to reduce their personal risk. The longer a Lawful Evil character is involved in their order, the more evil acts they have done and the harder it is for them to leave. If they leave, what will protect them from a society seeking justice?
A Lawful Evil system is put into effect by force. Anyone who doesn’t follow their code, acts out of line, or even is of a different race, class or social standing will face consequences. Lawful Evil characters feel no guilt or remorse for causing harm to others in this way. This is seen as the only proper means of maintaining order.

Lawful Evil. (LE) creatures methodically take what they want, within the limits of a code of tradition, loyalty, or order. Devils and blue dragons are typically lawful evil. -5e Basic Rules, Chapter 4: Personality and Background

It's nothing personal.
It's just about the contract.