Ronson hit back at River's comments about her ex-girlfriend, calling the 77-year-old a "bully".
Rivers told The Insider: "I think this ex-girlfriend, this DJ - I thought it was a skinny boy when I first saw the picture - came out doing jokes about me and [my daughter] Melissa. Why not worry about Lindsay Lohan? That girl is going to be dead in ten years if somebody doesn't take care of her.
"I suggest that this skanky little girl not worry about the jokes; worry about Lindsay. I find this insane that they are all feeding off of Lindsay. Maybe somebody should take care of Lindsay."
Lohan will begin a 90-day jail sentence on July 20 followed by a further 90-day stay in a rehab facility.
Rivers added: "Lindsay, I am pleading with you. you're beautiful, you're smart, you're talented. Go to rehab, you're young! My daughter Melissa and I will pay for your rehab!"