HOUSTON – A lawsuit filed by the family of a Galveston County inmate claims that he died from lack of medical care.

WATCH: Family holds news conference after Galveston County Jail death

According to an attorney for the family, Jorge Cortez, 57, was in jail for a probation violation. He didn’t know it at the time, but he was sick with mesothelioma, lung cancer, and experienced dizziness as a result.

Despite his dizziness, Cortez was required to sleep in a top bunk, even though he requested to sleep on a lower bunk said U.A. Lewis, the family’s attorney. Cortez fell off the top bunk, punctured his lung, and saw the jail’s private health care provider, Soluta, to provide medical care.

The family said Cortez was given ibuprofen, but his health continued to deteriorate so much that other inmates contacted them.

The attorney said Cortez went back to Soluta and was prescribed solitary confinement.

Cortez became immobile in the cell and was eventually taken to a hospital, where he died in the summer of 2017, according to the attorney.

"My father made so many outcries and was turned away," cried Cortez's daughter, Jacquelyn Burlingame Cortez,

during a news conference about the lawsuit Wednesday.

“He did not deserve to die. He was supposed to come home to us, to his daughters, to his grandkids. Galveston County Jail and their medical staff needs to be held accountable,” she said.

The attorney also referenced the deaths of five other people in the care of the jail's medical provider.

"Five deaths if five years -- there's no excuse for that," said attorney U.A. Lewis.

The plaintiffs are seeking compensation for, among other things, mental anguish, medical and funeral expenses and loss of inheritance.