Knox's stepfather said she saw part of the film on TV and was shocked. She told him she was hyperventilating, and she felt she was going to throw up.
"Amanda Knox: Murder on Trial in Italy," is due to air Feb. 21.
Knox's family has tried to block the film, saying it creates an "evil opinion" of their daughter while lawyers appeal her conviction.
The movie's star Hayden Panettiere defended the production.
"It's a very controversial topic, and I don't think people are going to have a problem with it," she said. "It's pretty fact driven, and it ends right when she gets convicted."
Knox's defense has given Lifetime TV one week to respond to its complaint before they take legal action to block the film. They also want a trailer removed from the network's website. The prosecutor on the case also said the movie should be stopped.
Lifetime is owned in part by Disney, the parent company of ABC7.