What does Lawful Neutral versus Chaotic Neutral divine interplay look like?

[Tanarii]

In the Great Wheel for D&D, Evil outnumbers Good by a large degree. The only reason they don't overpower the planes is they fight each other.

That means anyone concerned about maintaining The Balance will almost always be opposing Evil. Or at least making sure they keep fighting each other. If they're Good, they'll fight the Good fight, generally avoiding morally grey, and almost always avoiding outright Evil means. If they're Neutral they might use morally grey means when they believe it's called for, and may occasionally do outright Evil. Or they may even be Evil themselves, using any means necessary all the time.