When writing in third person…?
It depends on what tone you’re going for. Even third person has various levels of intimacy with the characters. If the POV is third person, but leans heavily toward Lana, I would probably refer to the character as Dad. That’s how Lana thinks of him, that’s how the reader is going to think of him. (If he’s not in the story much, you can get away with “her father,” but that gets awkward and cold if he’s on-screen very much.) If the POV is more distant from Lana– she’s the protagonist, but her emotions don’t really color the narrative– I would call him Paul. This means the story is approaching him as a person separate from Lana, not just as her father. So either one could work, depending on what you’re going for.