The 57-year-old was found guilty in June of murdering Ms Clay on March 20, 2020, but not guilty of killing her secret lover Russell Hill.
Lynn's barrister Dermot Dann flagged his client will appeal, indicating he had a number of concerns about the verdict and claimed the prosecution had conducted the trial unfairly.
"We submit that the long-term future of the guilty verdict must be seen as being in grave doubt," Mr Dann told the court.
He said his client maintains his innocence and maintains he told zero lies.
A formal application to appeal has not yet been submitted to the court, Mr Dann said.
Mrs Clay, 73, and Mr Hill, 74, went missing from the Wonnangatta Valley in Victoria's alpine region while camping.
Lynn pleaded not guilty, claiming the two deaths were accidental, but admitted burning the crime scene and destroying their bodies.
He faces a maximum penalty of life in prison.
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