Lane, 39, was found guilty in December 2010 of murdering her baby, two-day-old Tegan, on September 14, 1996, and is serving a minimum 13½-year jail sentence.

On Friday, justices Virginia Bell and Patrick Keane refused Lane’s application following a short address from her barrister, Winston Terracini, SC.

Mr Terracini argued that the NSW Supreme Court jury who found Lane guilty of murder should have been given the option of convicting her of the lesser charge of manslaughter.

"The jury was entitled to at least have an alternative scenario that, if you're not satisfied that she intended to kill or cause grievous bodily harm, you may be satisfied that some other criminal act took place falling short of [the intent required] for murder."

But Justice Keane said Lane’s lawyers ran a "guilty of murder or innocent" case.

"That's the way the case was put."

Justices Bell and Keane also told Mr Terracini there was "no evidentiary basis" for a case of manslaughter by unlawful or dangerous act.

"If it was an accident, your client was entitled to an acquittal," Justice Bell said.

The case was entirely circumstantial as Tegan's body has never been found and the Crown Prosecutor was not able to establish how she was killed.

Lane’s mother, Sandra, and Lane’s partner, Patrick Cogan, were in court to hear the decision. They declined to comment after the judgment.

Outside the court, Mr Terracini said he expected Lane would be disappointed with the decision, but he had not yet spoken to her.

Lane has maintained she handed over Tegan to the natural father, a man named either Andrew Morris or Norris.

But a nationwide search by police over many years failed to locate anyone who could be Andrew Morris or Norris, or any child who could be Tegan.

In December last year - three years to the day of the guilty verdict - the NSW Court of Criminal Appeal dismissed eight grounds of appeal.

Lane's lawyers took two of those grounds - that there was a "viable case for manslaughter" and that the closing address to the jury by Crown prosecutor Mark Tedeschi, QC, caused a miscarriage of justice - to the High Court.

Mr Terracini said the trial miscarried because Mr Tedeschi put 10 questions to the jury during his closing address which  Lane claims reversed the onus of proof in the jurors' minds. In particular, Mr Tedeschi asked them to consider why it took Lane four hours to drive from Auburn Hospital, where she gave birth to Tegan unbeknown to any family and friends, to her parents' house in Fairlight, where she arrived without the baby.

Mr Terracini said that, when the Court of Criminal Appeal acquitted Gordon Wood for the 1995 murder of his girlfriend Caroline Byrne, Mr Tedeschi's use of rhetorical questions was criticised as inappropriate and regretful.

"It's submitted that [Lane] didn't get a fair trial as a consequence of this rhetorical questioning going before the jury," Mr Terracini said.

He said Mr Tedeschi's conduct in Lane's case "wasn't as bad as in Wood but nevertheless it's the same sort of thing and it does create an impression that the onus of proof has reversed".

Justices Keane and Bell did not wait to hear arguments from the Crown but immediately refused special leave.

Lane has now exhausted all avenues of appeal.