How serious a crime is lying to the police & other law enforcement authorities?

What if you Mirandize yourself?

Not sure what you mean by this.

Anyhow, the way it works is that if you’re not under police custody you don’t need to be read your Miranda rights, of course. The cops are free to question you at will. However, you are also free to leave at will if you are not under arrest. The cops will often say something to this effect, that you’re not under arrest, but they’d like to question you.

Here’s a more precise explanation of your rights when being questioned by police.