Justice Ian Harrison declared in August 2022 that Dawson murdered his wife and disposed of her body on January 9, 1982 because he was infatuated with the girl.
The 75-year-old will try to overturn the conviction during a three-day hearing in the NSW Court of Criminal Appeal starting on Monday.
If his bid fails, the former PE teacher and Newtown Jets rugby league player is likely to die in jail after being sentenced to a maximum prison term of 24 years.
The jail stint will expire in August 2046 - when he would be aged in his mid-90s.
He will be able to apply for parole in August 2041 after his sentence was extended by a year when he was found guilty of unlawful carnal knowledge with the same underage student.
Because Lynette Dawson's body has never been found, laws preventing convicted murderers from being paroled until they disclose the location of their victims mean Dawson could be forced to serve the full term.
Dawson claims that Justice Harrison's findings were "unreasonable and unable to be supported", and that his guilt could not be shown beyond reasonable doubt.
He argues the judge could not have relied on alleged lies that he made at the time to show a consciousness of guilt.
There was also no way to definitively find that Mrs Dawson was not still alive after the purported date of her murder in 1982, he says.
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