Model Shaw, 26, has been picked to play the lead in new film Dogs in Pocketbooks and Michael Lohan is not happy.
He insists his Long Island neighbour Shaw, the daughter of infamous Patty Hearst, should concentrate on playing members of her own family before signing on to perform as others.
He tells X17online.com, "If people are that fascinated with Lindsay and our family, then great. But the Hearsts have an interesting background themselves, and I'd think they'd want to do a movie on their own family.
"I don't understand why... Lydia Hearst finds the need to make a movie about Lindsay and our family when the Hearst family probably has more drama than ours. Besides, how can you make a movie about a family when you don't have the facts?"
Lohan warns the filmmakers behind the project to tread carefully - or risk legal action.
He adds, "I smell more attorney fees brewing."
Screenwriter Charles Castillo tells the New York Post, "Lydia will play a bratty movie goddess in and out of rehab, in trouble with the law, and hounded by greedy agents, predatory paparazzi, off-the-wall stalkers and crazed media - a role obviously based on Lindsay Lohan.
"I spent a lot of time casting for the right actress for this screwball comedy, but Lydia is perfect. She's one of the few supermodels who can actually act. She's smart, well-read, charming and very beautiful. We looked at a lot of actresses for this role, and I was really knocked out."
Joan Collins is also reportedly onboard the project - as a Hollywood agent.
Hearst Shaw's mum Patty gained notoriety in the 1970s when she was kidnapped by the Symbionese Liberation Army (SLA). She eventually joined her captors and was arrested and incarcerated for her part in a bank robbery.