The lake is near the Whitby Shopping Village, is surrounded by a pathway, and is found close to a children's playground, library, Plunket centre and a church.
The man had singled out a paradise duck and trapped it at the base of two large trees, about 20m from the playground, the summary said.
"The defendant picked up the duck and has wrung its neck with such severity he tore the head from the duck's body," it said.
The man was photographed by a member of the public as he stood over the remains of the duck's carcass.
Police visited him at his home a little over a week later and spoke to him about the offending.
He admitted killing the duck and could not give an explanation for his actions.
At the time of the offending he was 18 years old and unemployed.
The man cried in the dock of the Porirua District Court today when he appeared.
He had pleaded guilty in July last year to one charge of ill-treating an animal. A separate charge of breaking a duck's wing has been withdrawn.
While sentencing was due to occur today, Judge Jan Kelly remanded the matter to April so a multi-disciplinary meeting could be held to address the man's "very high risk" of reoffending and safety measures that needed to be put in place.
According to psychological reports, the man has been diagnosed with autism spectrum disorder, and his mental health had been steadily deteriorating at the time of the offending.
"[His] situation is unique to his age with multiple underlying concerns," Judge Kelly said.
His high risk of reoffending would also escalate unless intervention was available.
While the man did not previously have name suppression, defence lawyer Michael Hay today applied to keep the man's name secret due to media presence in court, saying the case "cries out for a suppression order".
Judge Kelly granted an interim suppression order so parties could file submissions on the matter.