Heather’s husband Ian Wilkinson survived the poisoning.
Patterson was found guilty of murdering Don, Gail and Heather and the attempted murder of Ian Wilkinson in July.
In September, she was sentenced to at least 33 years behind bars.
The Herald Sun reports barrister Julian McMahon SC will represent Patterson in her appeal.
Her case has attracted national and international media attention.
She went through an 11-week trial, with a jury finding her guilty.
Justice Christopher Beale, in delivering his sentence, said her offending fell into the “worst category”.
The judge said Patterson showed “no pity” in the murders, adding: “Your offending involved an enormous betrayal of trust.
“Your victims were all your relatives by marriage. More than that, they had all been good to you and your children over many years.”
Patterson is serving her sentence in the maximum security women’s prison the Dame Phyllis Frost Centre.
The court was told it was likely she will remain in protective custody for the duration of her sentence because of her notoriety.
On the day she was sentenced, Ian Wilkinson gave a statement outside court thanking police for their investigation.
“They brought to light the truth of what happened to three good people,” he said.
“We are grateful for the truth that brought this to light. I’m also very grateful for the kindness and compassion they showed us, me and my family, throughout the process.
“We’re also grateful for the staff of the various public health services that played an important role in dealing with the aftermath of the lunch.”
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