Do truth and lies really have a purpose?

Do truth and lies really have a purpose when something such as belief exists?
By belief, I'm not talking about any specific type of belief. Example of the type of belief I'm talking about:

Person 1: I'm your real mother.
Person 2: I don't believe you.

Person 2 isn't saying that in accordance to the truth. The person is saying it according to what they believe to be the true.

Sometimes people ignore truth, and lies, according to their own judgement or belief. So are truth and lies really relevant when peoples own judgement/belief has a higher priority?

I see what you've done there.
I just can't understand why some people's beliefs can be more important or more accepted by others.

By it's definition, truth is not relative. But we make it so. We rationalize. We rationalize to make ourselves feel better, or more secure, or more important or whatever... We lie to ourselves.

We then expound our views to others. The more people that believe the same lie we do helps us enforce the lie we have told ourselves.

History has proven truth to be unpopular, even fatal.

This comment excludes the active reinforcement of another's lie. Example: "does this make me look fat"? You are not lying to yourself, but trying not to have the argument that will always ensue if you deny the lie of another.

If a statement is a misrepresentation due to ignorance, it is not a lie, but an innocent lack of knowledge of the truth.