Latimer arrived at Lothian's Te Haroto house at about 3am one morning in September 2018.
There, an associate of Webby and Lothian met him.
A new Court of Appeal judgment showed the two killers then ambushed Latimer, beating his head and hitting him with a shovel.
"Mr Latimer went quiet and a shovel was then thrown at him and he was ordered to dig his own grave," Justice Robert Dobson previously told Webby in court.
"You then resumed your attack on him, with each of you kicking, punching and hitting him with the shovel."
The Court of Appeal said Webby found out the associate who lured Latimer to the house had given information to police.
On a prison exercise yard wall, Webby dubbed the associate a "nark" and identified where he lived.
That led to a charge of attempting to pervert the course of justice.
Lothian was sentenced to life imprisonment with a minimum non-parole period of 20 years.
Justice Dobson said Lothian had done the stabbing and led Webby during the killing.
But he said the murder was "a two-man job" so Lothian and Webby could not have vastly different sentences.
Webby ended up with a 17 year, nine month minimum non-parole period. He said this was manifestly excessive, and it should have been nine months shorter.
But in its newly published judgment, the Court of Appeal said Justice Dobson was correct to take into account the brutality and callousness of the murder.
The appeal court also said Justice Dobson was right to point out that the murder happened in the course of aggravated robbery, another serious offence.