Lake attacked Roper, a flurry of punches leaving him on the ground.
Nuku instructed him to break the murderer's arm but Lake struggled to do so.
Frustrated with how long it was taking, Nuku jumped in, kicking Roper and putting him in an arm lock which eventually snapped the bone.
He tried to break the victim's other arm and both his legs but was unsuccessful.
Lake then punched him in the head several times as Roper lay there nursing his broken limb.
The 32-year-old also jumped in the air and stomped on the prone man's head three times, leaving him semi-conscious with a fractured skull.
Realising Corrections officers were not coming, Lake put Roper in the recovery position and sounded an alarm.
Roper was found guilty of killing Ms Tovizi after a High Court trial by either putting her in a sleeper hold or holding her head under water.
He then took her car and laptop, withdrew money from her bank account, and told family she had "done a runner".
He appealed against his murder conviction on several grounds: that his trial lawyer made errors, the judge admitted prejudicial evidence and failed to explain certain points to the jurors, and that Roper was unfairly prevented from sitting next to his lawyer during the trial.
The Court of Appeal rejected each of the grounds as having no merit.
Lake and Nuku will be sentenced later this month.
