When emergency services arrived at the house, several people were trying to give him CPR, but he could not be revived.
JJ lived at the house with his mother and her partner - not his father - and another couple with two small children.
Detective Inspector Scott Beard said yesterday that all six were home at the time of JJ's death.
No one had been charged over the death, but police had spoken to everyone who was at the house.
"The story we have from those at the address at the time is inconsistent with the injuries found at the post-mortem," Mr Beard said.
"At the time of the incident, we understand there were four adults and three children - including JJ - present.
"We need the adults to tell us all they know about what happened to JJ, for his and his wider family's sakes."
The Weekend Herald has learned that Child, Youth and Family was contacted four weeks ago by someone who had seen JJ and was concerned about his safety.
CYF officials went to his mother's house several times, but did not make contact with her. They did not see JJ before he died.
A CYF representative said JJ and his mother were not known to the agency until four weeks ago, but would make no further comment on the case, saying police had requested all inquiries go through them.
Mr Beard said the investigation was ongoing and child abuse cases often took "some time".
He refused to say where in the house JJ died, or where he was when police arrived.
He said officers had finished their scene examination and the house would be handed back to JJ's mother when she returned from his tangi, which was held at Kaeo in Northland on Thursday.
Police had also completed an area canvass and had taken statements from many of JJ's neighbours.
Mr Beard said what went on "behind closed doors" was often not heard by others. But he urged anyone with information to come forward.
"Anyone with information that might or could assist should consult their conscience and call police," he said.
Members of JJ's family did not respond to messages this week.
But they set up a Facebook page in his memory.
On Thursday, a relative wrote: "Little James was laid to rest today. Rest in peace little one. May you saw [sic] the skies and find the light, your are a much loved wee boy".
Earlier, his aunt wrote that he was a precious child who brought light into the lives of his family.
"Your daddy loves you so much and is devastated and lost without you. You were the most amazing child and obviously too beautiful for this world."
This week, neighbours told of hearing a woman screaming just before police arrived at JJ's home.
Te Pokuru Titoko said the woman screamed: "What did you do? What did you do?" to which a man yelled back, "I don't know."
The woman then screamed, "I hate you, I hate you."
A man replied, "Sorry."
Can you help?
If you have information about the death of 2-year-old James Joseph Ruhe Lawrence contact:
* Police Operation Avalon team, (09) 524-1925
* Crimestoppers anonymously, 0800 555-111
