The 31-year-old, listed in court documents as having no fixed address, was arrested on September 24 for charges of murder and sexual violation.
Harrap disappeared on September 22 while on her daily walk. Her body was discovered hours later along a bush-lined walkway, about a kilometre from her home.
The 27-year-old was active in StarJam, a non-profit which gives those with disabilities an opportunity to perform.
"Lena may have been small in stature but she had the biggest heart," Lynfield College principal Cath Knell said last month.
"Her wicked sense of humour backed up by a mischievous smile brought much joy to those who taught her."
Sexual violation carries a maximum punishment of 20 years' prison, while murder carries a life sentence.
Favona murder-accused also fit
Justice Fitzgerald also on Wednesday issued a similar ruling for a South Auckland man charged with murder for the September death of 72-year-old Mohammed Hakim.
The judge reviewed two psychological reports before deeming the man not unfit to stand trial.
He will continue to have name suppression as other mental health issues are investigated.
The defendant did not attend the latest hearing but not guilty pleas were deemed by the court on his behalf. A trial date was set for May 2023.
Police were called on the evening of September 21 to a Favona property, where they found Hakim dead. Authorities did not say if the two were known to each other.
The homicide investigation was launched one day before Harrap's death.
