Also pleading guilty to charges of assaulting another man and damaging his vehicle at Mohaka two nights earlier, Lambert was remanded by Justice Robert Dobson in custody to appear for sentence on November 27.
Counsel Susan Hughes QC asked the judge to refer the matter for restorative justice and said a cultural report would be provided ahead of sentencing.
Family of Lambert and Huata packed the public gallery as the charges were put to Lambert, with a woman from the victim's family calling out: "Look at what you've done to my family. You can't even look my nan in the eye, you coward."
As he was being led to the court holding cells, one of Lambert's family called to him, "love you my bro'!"
The two men had known each other for many years and the shooting was said to have happened after they arrived separately at the rural address, a few hundred metres from the now empty site of the former Mohaka Hotel.
Lambert was said to have waited in the dark and watched until Huata exited a house on the property, and then confronted him about another person thought to be at the address.
It was in that confrontation that the shooting happened, Lambert driving from the area afterwards, abandoning the car, walking across farmland and disposing of the gun in a stream before walking home.
He was arrested more than a week later after telling police he was the gunman.
The trial was originally set down for two weeks but by this week, was expected to take just two days.
