But Aleksander Vojneski, 32, must first convince the ACT Court of Appeal to grant him leave to appeal out of time, before he can then challenge his murder conviction and life sentence.

Vojneski was found guilty and sentence to life imprisonment for the murder of his girlfriend in March 2012, inflicting 15 knife wounds on her in the bedroom of her Macgregor home.

No clear, direct motive emerged from Vojneski's trial, but evidence suggested he was becoming increasingly desperate to get drugs on credit on the night.

Vojneski, an ice-addict with significant mental health issues, had a tendency to become violent when he didn't get drugs, and had used knives in attacks and threats in the past.

The convicted killer initially only appealed his sentence on the grounds it had been manifestly excessive.

But Vojneski's barrister, Shane Gill, said evidence of his tendency towards violence should not have been allowed and caused unfair prejudice to his client.

Mr Gill said the delay in lodging the full appeal had been due to a change in legal representation.

He told the court a new grant for legal aid and research time also caused the 28 day deadline to expire.

But ACT Director of Public Prosecutions Jon White opposed the application, arguing the delay could prejudice the prosecution case.

Mr White said the passing of time "diluted" memories and prolonged the suffering of loved ones of the deceased.

"That's why we have time limits. Any delay has the potential for prejudice," he said.