The High Court at Wellington confirmed this morning that Lundy's lawyers had filed a bail application and a hearing was scheduled for Friday afternoon.
Lundy will not be appearing.
Lundy was convicted of murdering his wife Christine and daughter Amber in August 2000 and sentenced to a jail term of at least 20 years.
His case was taken to the Privy Council and a three-day appeal hearing was held in June.
In its decision - released on Monday night - the Privy Council unanimously decided that Lundy's appeal should be allowed; that the convictions should be quashed; that Lundy should stand trial again on the charges of murder as soon as possible; and until then, and subject to any High Court decision on bail, Lundy should remain in custody.
A Crown Law spokeswoman would not say whether bail would be opposed by the Crown. She said it would be inappropriate to debate the issue through the media.
Christine Lundy's brother, Glenn Weggery, who found the bodies of his sister and niece after the murders, last night expressed how he felt about the Privy Council's decision on Facebook: "Bloody stupid Privy Council. Yet again the victims are let down by the 'justice'`system!!"
