Roberta wanted the court to halt the auction until after the royal commission into Victoria Police's management of the gangland investigations, which will include the force's dealings with Informer 3838.

But Justice Steven Moore on Friday said although Informer 3838 was George's lawyer between 2003 and 2007, there was no evidence she gave him any advice on settling his tax debt with the ATO.

That meant Roberta's application to the court was overstated, "fundamentally speculative" and could not be accepted.

Roberta had argued the facts an ATO investigator worked with the police who investigated Victoria's gangland crimes, and that Informer 3838 worked with the Purana taskforce warranted further questions.

But Justice Moore said those links did not take Roberta's case beyond a hypothesis and speculation. He dismissed her application for an injunction halting the auction.

He said if the royal commission unearthed evidence Informer 3838 advised George on the tax debt, then Roberta would have the option of suing the lawyer.

Dhakota, Roberta and two supporters walked out of the court room as Justice Moore was discussing the issue of costs, which will be finalised at a later date. They declined to comment.

Dhakota, 17, lived at the house for most of her life, the court heard, but handed the keys over to the ATO in September, following two rulings this year by the Supreme Court that found Roberta and her daughter had no claim to the house and that the property should be sold off to cover George's tax debt.

The house has a reserve price of $750,000 but is understood to have been valued at about $1 million.

Roberta said in an affidavit tendered to the court she and her family were "couch surfing due to the family's limited means".

"We are relying on the generosity of friends and family to provide us with a roof over our heads," she said.

While in prison for murder, Carl Williams negotiated to have his father's tax reduced in return for giving information to police on other underworld killings. But police later reneged on the deal.

Carl was bashed to death in prison in 2010.