An Australian woman facing the death penalty in the US over the death of her stepdaughter was let down by the health system, the woman's lawyer claims.

Former South Australian resident Lisa Cunningham, 44, and her husband, former police detective Germayne Cunningham, have pleaded not guilty to 11 charges, including first-degree murder and child abuse, in the US state of Arizona.

Sanaa Cunningham died in February, 2017, aged seven. ( Supplied: )

Mr Cunningham's daughter Sanaa, 7, died in February 2017, with an autopsy finding the cause of death to be sepsis related to a chest infection, an abscess in her right foot and multiple skin ulcers. It was also noted the child had an unspecified schizophrenia spectrum disorder.

Court documents allege the couple shut Sanaa in their backyard, laundry and garage, forced her to sleep outside, restrained her with cable ties and failed to seek medical care.

In August the Maricopa County Court ruled that both adults were eligible for the death penalty, remanding them in jail.

In an exclusive interview with 7.30, Ms Cunningham's lawyer Eric Kessler said the couple had tried their best with Sanaa but were overwhelmed by her mental illnesses.

"Sanaa presented with very difficult medical, emotional and psychiatric issues. They sought professional care in all of those fields. Even when they had limited funds, they nonetheless continued to find a solution for Sanaa," Mr Kessler said.

Mr Kessler said the family had been let down by the system.

Lisa Cunningham's lawyer, Eric Kessler. ( ABC News )

"If even one medical professional or mental health professional had properly diagnosed this child and given appropriate instructions to Lisa and Germayne to deal with Sanaa's true problems, then I don't believe we would have a deceased child," he said.

Mr and Ms Cunningham each had two children from previous relationships, then had two children together.

"Lisa loved Sanaa as though Sanaa was her own," Mr Kessler said.

"I can see from their other children who are well-adjusted and healthy ... so I take from that that they're excellent parents."

It will be two years before the case goes to trial.

Ms Cunningham is currently being held in Estrella, a women's jail in Phoenix.

Text messages allegedly reveal daughter was tied up

Prosecutors paint a very different picture of the Cunninghams.

7.30 has obtained police detective's Noah Yeo's harrowing court testimony about Sanaa's home life and mental health.

Sanaa Cunningham, pictured far right, with her five siblings. ( Supplied )

"Ms Cunningham expressed to us that Sanaa had been self-harming ... she used to restrain Sanaa. What she described as protecting her, was to place a long-sleeved sweater around her arms, similar to a straitjacket style, where her arms were crossed over her chest," the detective said in court.

Text messages between Mr Cunningham and Ms Cunningham are key to the prosecution's case.

"In these text messages they specifically talked about being fed up with Sanaa and putting her in a garage and zip-tying her to a large water container," the detective told the court.

The detective also told the court what he saw during the autopsy.

"Sanaa Cunningham, from my observations, had cuts, bruises, scarring to the bottom of her feet, to the top of her head, over her entire body," the detective said.

The court heard the Cunninghams were concerned about the effects of an anti-psychotic medication a doctor prescribed for Sanaa in the leadup to her death.

Ms Cunningham's lawyer told 7.30 "they never intended any harm for this child".

"In fact they went out of their way, and through extraordinary means sought help from any number of sources, whether it be from the government, private medical facilities and so forth.

"Towards the end, just shortly before Sanaa died, she saw medical professionals whose evaluation and treatment is suspect."

'Prosecutors said the defence is a pack of lies'

Arizona in America's south west — best known for the Grand Canyon — is one of the 31 US states that still has capital punishment.

Phoenix-based freelance journalist Sean Holstege said the state prided itself on a hard-line approach to law and order.

Journalist Sean Holstege has been following the case. ( ABC News )

"Currently Arizona has 117 people on death row. If Arizona puts Lisa Cunningham to death as a result of a successful conviction in this case, she would be the first Australian woman ever executed in the United States," he told 7.30.

The Cunninghams were indicted in December last year.

"Prosecutors have said that the defence is a pack of lies, frankly," Mr Holstege said.

"They have said the Cunninghams have tried to manipulate the record and manipulate the diagnoses. They went doctor shopping, is the term that they used in court."

The charges come amidst a series of child protection failings in Phoenix, and questions about whether Mr Cunningham's job as a police officer initially afforded him special treatment, and later made him a target.

"The first official record that Sanaa was having any problems at all came in April 2016, and that is when somebody reported suspicions of neglect," Mr Holstege said.

"Germayne Cunningham showed them all the medical records suggesting that he was trying to do something about that condition, and they concluded that he was and basically closed the case."

Lawyer Mr Kessler said Ms Cunningham believed the charges "are not the kind of charges that would normally be brought against parents, but that there may be other factors at play here, be they political or otherwise, that resulted in the government bringing these charges".

Ms Cunningham's lawyers are seeking help from the Australian Government to defend the case with financial aid, which has been given to other citizens facing serious charges abroad.

"The Australian Government has not been terribly receptive," Mr Kessler said.

"We're in the process of trying to schedule meetings with the Australian Government so at this point I can't criticise their efforts."

The Attorney-General’s Department declined to comment.