Gebhardt pleaded guilty to the manslaughter charge in the High Court at Christchurch today.
Justice Cameron Mander remanded him in custody for sentencing on August 3. He ordered a pre-sentence report and victim impact statements and gave Gebhardt a first strike warning.
Defence counsel Andrew McCormick said Gebhardt did not seek bail ahead of his sentencing.
Crown prosecutor Mark Zarifeh told the court Gebhardt had shared custody of Lachlan with his ex-partner.
On November 5, 2019, Gebhardt arranged with Lachlan's mother to pick him up later than usual from a swimming pool in Rangiora.
He picked him up from his grandmother at the pool and they left at 4.08pm, with Lachlan sitting in the back seat.
Gebhardt drove at speed along Lehmans Rd, faster than the posted 80km an hour limit. He swerved sharply when he passed a vehicle and had to get back to avoid an oncoming vehicle.
At the end of the straight, there was a right-hand corner with a posted 25km an hour speed advisory.
Police estimated his speed at about 130km an hour when he reached the turn, but he made no effort to slow or swerve.
The car hit the speed sign, went up a bank and became airborne for 24m before it hit a tree 7m higher than its take-off point.
The car caught fire. Members of the public called for emergency services and then pulled open the passenger door and dragged Gebhardt out.
The fire prevented them from getting back to the car.
Gebhardt told them he wanted them to put him back in the car because he wanted to swap places with his son. He said his son was "such a nice boy".
Gebhardt said he "wanted a bullet".
Zarifeh said Gebhardt received burns to 30 per cent of his body, a fractured femur, and facial injuries. Lachlan died at the scene.
When he was interviewed by the police about seven weeks later, Gebhardt said he could not recall anything about the crash.
In September 2020, 10 months after the fatal crash, he walked into the Christchurch Police Station, took his clothes off and pleaded to be jailed.
He was arrested and charged with obscene exposure in public.
At a court appearance soon after, McCormick explained that Gebhardt was "having difficulty" with trauma issues.
However, Gebhardt insisted on pleading guilty immediately, and was jailed for a month for the obscene exposure offence.