'Akosita and her husband, Etuate were jailed in 2021 for corruption and fraud connected with a school they ran.
In 2022, the Court of Appeal overturned the original sentence rule the judge in the earlier trial had not been impartial.
The Court of Appeal then ordered that the duo be retried in the Supreme Court.
Ahead of that retrial 'Akosita Lavulavu had asserted Justice Langi would show bias because she had been working at the Attorney General's office when the charges were first laid against the Lavulavu's nearly six years ago.
Lavulavu was seeking leave to appeal after Justice Langi had declined an earlier application to recuse herself from presiding over the re-trial.
The Matangi Tonga website reports Justice Tony Randerson stating he had no hesitation in concluding that this appeal had no merit.
He said there is nothing to suggest the judge will not deal with the case fairly, objectively and in accordance with her judicial oath.
The Lavulavu's were chargely over allegedly fraudulent claims for $US250,000 in government funding given to their private school, "Unuaki 'O Tonga Royal Institute, to cover student transition.
The school had claimed in 2013 to have 255 eligible students when there were only six; in 2014 the school claimed for 416 students when there were only nine; and in 2015 they claimed for 271 students when there was only four eligible.