My mom's boyfriend is such a liar. How can I call him out the right way without looking like the bad guy?

My mom's boyfriend is such a pathological liar. He says that I lie about serious things, when I don't. He says I do things I don't. My mom always believes him because she thinks it's obligatory. He ALWAYS makes things up. My mom always believes him and blames his obsession with lying on me. I know why he does it. He does it to make me look like the bad guy and so that I get punished for what he does. When I try to call him out, he ends up lying AGAIN and my mom believes him. When I try to tell my mom, she doesn't believe me and dismisses his behavior. She punishes me with extreme sanctions, like not letting me talk to my boyfriend, a boy I'll call Ilia*, on the phone because he says so and WHAT HE SAYS GOES in my dysfunctional household, even if he's lying. When I talk on the phone with Ilia*, we compare him to a tyrannical dictator because he twists it around to make innocent people look like the bad guy. Ilia* tells me to call him out when he's lying. Should I listen to Ilia*? If I call my mom's boyfriend out when he lies, how can I do it the right way without looking like the mean girl or the bad guy?