So that means a liar is something defined on the side of the subject, while falsehood is on the side of the object (maybe relative to the idea of the sphere). Is there harm here in some moral sense (if we define morality as depending on ideas)?

I didn't understand the question.

When a person lies, is there some moral problem even if he isn't a liar?

I don't understand. He lies and yet isn't a liar? Do you mean that what he says isn't true? The only problem is being a liar. Of course, it's proper to check things before you say them.