Justice Betty King said on Tuesday it was unacceptable that Legal Aid was unable to continue a pre-sentence hearing on Monday for Scott Allen Miller after his defence lawyer Stephen Payne fell ill and had to be taken to hospital.

Justice King said Miller's junior counsel should have been able to step in immediately and take over the case.

The judge vowed to take up the issue with the Chief Justice as she believed Legal Aid should have briefed two barristers, not two less-expensive lawyers, to represent Miller for what was a very serious case of murder, which she had described as "every woman's nightmare".

She told Legal Aid chief counsel Sam Marsh she was very concerned about the situation and it should never happen again.

Justice King apologised for the delay to the family of the victim, Renea Lau, who had travelled from Hong Kong for the court hearing, and promised to do her best to try to sentence Miller before the family had to return home on Saturday.

Mr Marsh told Justice King that Mr Payne had been taken to hospital on Monday afternoon but found to have no serious medical issues and was now resting at home.

A spokeswoman for Victoria Legal Aid said she was confident that the defence of Miller's case had been well prepared to this point. The "need for a short delay of a day was brought about by the unforeseen illness of (Mr) Payne who collapsed in court and was taken to hospital by ambulance," she said.  

The organisation had "rigorous processes in place to support the briefing of in-house lawyers and... private practitioners and barristers who undertake the majority of legally aided criminal cases," she said.

"It would be unusual and expensive to have two senior public defenders or barristers allocated to a case. Generally the options for representation in a criminal law matter are counsel and instructing solicitor, or two co-counsel - senior and junior barrister."

Both of Miller's lawyers are solicitors working in Victoria Legal Aid's in-house public defender team. Mr Payne is one of its senior public defenders with over 20 years' experience, and his junior counsel in the case is a solicitor-advocate.

Miller, 43, has pleaded guilty to one charge of murder and two counts of rape after he chased Ms Lau over St Kilda Road and attacked her in parkland. Miller had been ejected from a bar and Ms Lau was on her way to work when their paths crossed at 5.26am on June 28 last year.

Ms Lau, 32, a Chinese national, had been at choir practice the previous night and was on her way to work at Ganache Chocolates in South Yarra when she encountered Miller and was so frightened she ran across St Kilda Road.

Miller was homeless and sleeping rough in the weeks before the murder, and in the lead-up had spent more than seven hours in two city bars, where he had consumed alcohol, harassed several women and offended several other patrons.

Patrons in Transport Public Bar, in Federation Square, and The Carlton, in Bourke Street, had described him as rude and obnoxious, although he did not appear overly affected by alcohol or affected by drugs.

He was ejected by security staff from The Carlton at 5.07am and walked through Melbourne's central business district and along St Kilda Road, where he encountered Ms Lau and chased her.

"The prisoner caught Renea and a struggle ensued in the centre island of the southbound traffic," Crown prosecutor Michele Williams, SC, told the court.

"In an attempt to fight off and escape from the prisoner, Renea scratched the prisoner's forehead above his right eye. Still fighting, Renea was dragged then from the centre island across the roadway, into Victoria Police memorial, leaving finger scrapings in the dirt of the centre island."

Ms Lau was repeatedly punched to the face, had her head smashed on concrete and force was applied to her neck. Miller then twice raped her and left Ms Lau's body at the scene, with clothing on top of her.

An autopsy revealed the cause of death was asphyxia.

The pre-sentence hearing will resume on Wednesday.

With Jane Lee