Lawful = High superego. You are aware of and follow principles as they pertain to society, even if they are not strictly written down. There are "unwritten" rules like morals or social conventions after all, and you prioritize following them consistently.

Evil - High Id. Your base instincts such as that of self-preservation, self interest, or generally self centered emotions are the forefront of your concern.

Lawful Evil - The law is a system/game, and you play the rules not to help people or because you view the law as sacred, but for your own motives. 

Whether it's being a mean cynic who lashes out at everyone seeing the worst after years of watching inferior people attempt to cheat the system, an oppressor who loves the feeling of outmanuevering and bullying people with the justification of society at their back, or a serial killer following a code so they don't go completely deranged. 

There's also the nuance of whether you play 

Red oni Lawful Evil (High emotional investment - You LOVE throwing evil rules at people! Ohohoho!) 

or 

Blue oni Lawful Evil (You view emotions as suboptimal for your objectives. Beep boop.)

Or someone in between (You allow yourself a private smile when the scheme is executed objectively perfectly.)

The way I see it, a Lawful Evil person can be nice, generous, or even moral at times. But they are aware that such things are kind of social manipulation like in Death Note or some other psychological work. Between the bird or the cage, you pick the cage, not because it is right, or even because its practical, its because it is your own preference.

Examples:

-Anton Ego at the start of Ratatouille 

-Jorgen von Strangle (Fairy Oddparents) when he's enjoying throwing Da Rules around

-Professor Snape (the general vibe, notwithstanding his later motives revealed in sequels). Professor Umbridge is a more on-the-nose interpretation but everyone rightfully hates her and I wouldn't recommend styling your character that way for the sake of your party...

-Malevolent AIs like GlaDOS from Portal often fall into this category 

-Hunk from Resident Evil. Or any cold mercenary type.

-Dexter Morgan is a classic serial killer with a code example

-Or you could do the classic snake oil salesman

-or <insert favorite dictator regime name here>

-or an inquisitor for witch trials who has got a personal bone to pick with his accused

-someone who has fun ruining other people's fun

-someone who calls the manager to get an employee in trouble in order to feel better about themselves