No dates have been set.
The Court of Appeal said it has not received any appeals in relation to Martin.
The trial heard how the pair met Lomax at a cemetery under a guise related to drugs before driving to a secluded area by the Waimakariri River on September 4, 2017.
Gosset later told police he knew it would be a "one-way trip" for Lomax.
Fuelled by methamphetamine, the pair unleashed a slew of gunfire in a "cruel and callous" attack, the court heard, that left the victim unrecognisable.
"Mr Lomax was shot once in the knee, which caused him to be incapacitated, before likely being shot in the chest," Justice Mander said.
"Neither wound would have killed him instantly."
While he was lying on the ground incapacitated he was shot in face twice from close range, he said.
"During this time, he was also wounded in the head as a result of a succession of shots fired from the .22 firearm."
Lomax's body was left at the riverbed, his face effectively "obliterated and unrecognisable".
The 24-year-old's death caused incalculable hurt to his family, Justice Mander said.
"His family must live with the loss of their loved one forever," he said.
"The nature and circumstances of his death have understandably been a particularly difficult burden for them to bear."