The three Melbourne men were convicted of being involved in a terrorist plot to attack the Holsworthy Army Barracks in Sydney. Justice Betty King sentenced them in 2011 to 18 years' jail.

One of the men, Nayef El Sayed, appealed his conviction and sentence in the Court of Appeal on Thursday. Another, Saney Edow Aweys, was also in court and the third, Wissam Mahmoud Fattal, appeared via video link.

Justice King denies the allegation.

Former solicitor Vu Anh Huy Nguyen said he was in a lift with Justice King and his barrister at the Owen Dixon East chambers in Melbourne on October 1, 2010, before the accused men's lawyers had begun presenting their defence.

Mr Nguyen had been visiting his barrister, Peter Murley, in his chambers before he was committed in the Melbourne Magistrates Court to stand trial for allegedly obtaining a financial advantage by deception. He was acquitted in 2012.

Justice King greeted Mr Murley and then said "I'm going to lock up a terrorist" or words to that effect, the appeal court heard.

Mr Nguyen said he recognised her from television appearances and that Mr Murley confirmed her identity after she left the lift.

Mr Nguyen could not remember the context of the remark or its exact wording. But when pressed and asked in cross-examination whether he acknowledged he might be wrong, given the judge's denial, he said: "Definitely not, sir. Those are the words that I heard."

He had been "disturbed" by the remark and had told Mr Murley at the time that he thought it was inappropriate for the judge to say it.

Mr Murley, who was said to be the only other person in the lift, has said he cannot remember the exchange.

Mr Nguyen was later struck off the roll of legal practitioners after pleading guilty to charges of theft, false accounting and deficiency in a solicitor's trust account.

When he was sentenced, Justice Paul Coghlan said his crimes were "largely those of a thoroughly disorganised person, rather than an outright dishonest one".

Theo Alexander, for Sayed, said that despite the fact Justice King was a Supreme Court judge "we are all human" and that it was impossible to test the exact probability she would make the alleged remark "because we are not able to explore the proclivities of the judge". Justices Peter Buchanan, Geoffrey Nettle and Pamela Tate did not have to decide whether Justice King had actually made the remark, only that there was a "real possibility" she had.

"Unless there's ... headway made in cross-examination which demonstrates he is motivated by malice against the courts or some individual malice, there's nothing about what Mr Nguyen has said to this court to sustain a view that the comment was not made, which expresses, by its very nature, the real possibility of pre-judgment," he said.

Prosecutor Nick Robinson, SC, said it was "improbable" a Supreme Court judge would make such a remark "in the presence of known counsel".

"It couldn't be more notorious in the sense of the operation of law in Victoria that clients of counsel regularly travel in lifts in Owen Dixon," he said.

Mr Robinson said Justice King could have been referring to the way the trial was going rather than to her pre-judgment, because she had not referred to a particular accused person and two people accused of being involved in the terror plot had been acquitted beforehand.

The judges reserved their decision.