The case featured on Police Ten 7 last month and Lendrum said the publicity had generated new information from the public.
He urged anyone else with information to come forward.
"There are people out there who know who is responsible for Chris' murder and we continue to encourage anyone with information to contact Counties Manukau police," he said.
"You may think that your information may not be significant to the case, but it is important for anyone with information to come forward as it could hold vital clues for the police investigation."
Can you help bring Chris Bush's killers to justice?>
If you have information about the murder of Chris Bush in 1987, contact the Counties Manukau police on (09) 263 2791 or Crimestoppers on 0800 555 111.