Lindsay Lohan -- I'm Keeping My Lawyer ... The Media Lies!!!

Lindsay Lohan doesn't care that the judge in her criminal case and the media have called her lawyer incompetent ... she's sticking with him.

Sources close to Lindsay tell TMZ ... she's angry that the media is painting Mark Heller as a nincompoop. She says, "It's all lies."

What's more ... Lindsay doesn't care that Judge James Dabney also called Heller incompetent to practice in California. In fact, the judge was brutally honest ... to the point he said if Lindsay keeps Heller, he'll order her to court for the next hearing to explain why she would be waiving her right to a lawyer who knows what he's doing.

As we first reported ... Michael Lohan reached out to his daughter and offered to pay for a new lawyer, but she turned him down flat.