"That is not what the people of Hastings signed up to when they elected him mayor".
It is understood three others have put their names forward for the National party nomination. The selected candidate will not be announced until late February.
Ms Lorck said that regardless of whether Mr Yule was selected, he had essentially told residents he did not want to be mayor of Hastings.
"He's checked out," she said. "He might not be a man of his word, but if he has any integrity left he will stand down now."
The Hastings resident said she had "nothing personal" against Mr Yule wanting to become an MP, but was disappointed "that in a year when Hastings needs its mayor the most, he's walked away, after just three months ago committing to a three year term".
"The political circumstances have changed for National but the challenges facing Hastings today are the same as they were when he took the job and they will be the same tomorrow and when he's gone."
She said a new mayor needed to be elected as early as possible so they could serve out the rest of the term.
"We can have every confidence that our deputy mayor Sandra Hazlehurst can lead the strong new council in the meantime," she said.
"The cost of a byelection is a big price to pay for Lawrence's decision, but it is important that we turn this into the opportunity now to invest in a new mayor for Hastings."
Ms Lorck's partner is Hastings district councillor Damon Harvey.
Mr Yule said he was not prepared to discuss such matters until the nomination was confirmed in February, but added that he had no intention of standing down now.
He said issues such as a byelection, his resignation, and whether or not he takes leave without pay were all matters to discuss at the end of next month.
He reiterated his commitment to resolving Hastings' water issues.
"I'm not about to walk away from that because Anna Lorck thinks I should."