A MOTHER who left her daughter to die from starvation is appealing her murder conviction and life sentence, claiming the jury was not properly instructed about how to interpret lies she told after her daughter's death.

The seven-year-old, who became known by her middle name, Ebony, deteriorated from a chubby, healthy child to die in the bedroom of her Hawks Nest home in November 2007, weighing just nine kilograms.

Her mother, 39, who cannot be named, was convicted of murder and sentenced to life in prison in 2009, with the sentencing judge describing her as ''unimaginably heartless and cruel''.

But in the NSW Criminal Court of Appeal on Friday, the woman's barrister, David Dalton, SC, argued that the trial judge had not properly instructed the jury.

The woman had said at her trial that she was unaware that her daughter was close to death because she was heavily drunk and affected by large doses of prescription drugs.

The prosecution countered that the woman had known, and had told lies after the murder to conceal the fact, including telling police that she had fed and watched television with Ebony shortly before she died, and then helped her walk to her bedroom.

Mr Dalton said that under the law, the jury was only allowed to consider these lies in terms of the woman's ''general credit'' as a witness, not as proof that she was a murderer.

The trial judge, he said, had not properly informed the jury of this point and therefore their verdict was based on a misunderstanding. ''The [prosecution] case was run on the basis that she told these lies because she knew that the child was going to die,'' Mr Dalton said.

Members of the three-judge appeal panel expressed reservations about this argument.

''The judge made it very plain to the jury that they weren't to use the evidence of lies [in determining guilt],'' Justice Peter Hall said. ''His honour couldn't have made it any clearer.''