I guess chaotic neutral is you don't pick sides but you make things go a little crazy... and the lawful evil is like corrupt guards, like in that one oblivion quest.
you do not pick your Alignment in elderscrolls games like you do in D&D. He is asking more about your play style. Elder Scrolls is normally great with the quest in their games. ((oblivion removed roleplay from the game thanks to the quest marker. Which removes the choses you can do per quest.))
What he is asking is when your quest give you a chose. What will you do?
Here is an example from morrowind. You find an excape slave. What do you do.
A.) Take him to the underground place that helps free slaves.
B.) take to the slave capital and sell him.
C.) Kill him for being an excape slave.
Then you have to think. If you chose A.) What do you do next?
Do you tell the gaurd about the free slaves? Do you let them be? Do you kill them all?
Your Alignment is based more about your actions. Your actions will give you points in Fame and Infamy.
I hope you have a better idea of what he is asking. If you need more help here is a link for you. The website has some examples of fictional characters that fit is role.
http://en.wikipedia.org/wiki/Alignment_(Dungeons_%26_Dragons)
FYI I think batman is more lawful evil and not lawful good. After all he is a criminal. superman is Lawful good.