deserve,  Teare wrote in the filing.

Gilley has claimed to the Italian court during previous proceedings that he was wrongly accused, doesn't have faith in the justice system, and that he fled the U.S. to avoid being killed while seeking protection in Italy.

The Italian court held another hearing on the extradition case Wednesday and reserved its decision to make a ruling in the coming days, according to attorneys familiar with the court proceedings.

 The goal of the lawsuit is to hold Lee Gilley accountable and to prevent him from recovering assets,  the Bauers' other attorney, Badge Humphries, said.  Whether or not he'll be held accountable by the state of Texas depends on whether they can work out his extradition with the Italian Republic. We plan on holding him accountable through this lawsuit regardless. 

In an op-ed published this week by The Wall Street Journal, Christa Bauer's parents, who noted the family's Italian heritage, announced publicly for the first time that they don't want the death penalty imposed in this case.

 We don't believe justice for Christa involves taking another life. For us, justice means improving the well-being of women like her. It means confronting the global problem of violence against women. Italians have come together in recent years to reject violence. In November, the Italian Parliament unanimously passed a law that defines the crime of femicide and makes it punishable with a life sentence. Italians have made clear they don't want to harbor those accused of violence against women. On the second anniversary of Christa's murder, an Italian court will again consider Lee's asylum plea. We are asking that Italian and U.S. authorities work together to grant extradition. Our family doesn't seek Lee's death. We seek justice for Christa's,  Chris and Sharon Bauer wrote.

The wrongful death lawsuit also seeks damages for Chris and Sharon Bauer, the two surviving children and her estate, plus exemplary damages.

Humphries said they plan to request that Gilley's other attorneys accept service of the lawsuit on his behalf.