In my experience with Lucifer, he never lies.

He may only show you part of the truth. He may answer your questions with replies that are technically true, but still misleading because you’ve asked the wrong questions. But he doesn’t lie.

The Lightbringer exposes the truth with his pitiless brilliance. He shows you reality in all its ugliness, and sometimes, surprising beauty. And he tells the truth even when it’s painful, even when it hurts, even when it threatens to upset your entire worldview or drive you insane. 

And I think that is precisely why they call him the Father of Lies. Most people don’t like the truth. Truth can be harsh and cruel and upsetting. Tell too much truth and you won’t have many friends, in time. 

They fear the truth, so they call him a liar.