An intensive land and water search continued yesterday for Lucas, who has not been seen since wandering off from his grandmother's home in suburban Kaiti about 3pm on Tuesday.
A police dive squad scoured the Waimata River for him again yesterday, and people continued searching the area including the riverbank near Lucas' home and surrounding streets.
Police were also out door-knocking around the Kaiti area, and have appealed for people to check their properties for the blond-haired Caucasian boy.
The family was "incredibly grateful" for the wonderful support from the community and from friends and family, his parents, Jessica and Damon Ward, said yesterday.
"Lucas is loved by all of his family and we are missing him dreadfully, especially his eight-year-old brother, Alex, and 14-year-old sister, Raegan," they said.
"The response from caring people is keeping our hopes up."
They were not giving up on Lucas being returned to them soon.
It was important people continued to check their properties, sheds, vehicles, boats or other places "curious kids might hide", Gisborne area commander Inspector Sam Aberahama said.
"We must remain optimistic of finding Lucas but as time passes we also acknowledge our concern for the well-being of this little boy. He is a smart wee boy who could be looking for a way home," Mr Aberahama said.
"We have no indication of foul play, but are very worried that Lucas has had an accident, could be lying injured somewhere or has got trapped somewhere."
Lucas was wearing navy blue track pants with two orange stripes down both sides and a light blue sweatshirt when he went missing. He was barefoot.
"Please help us find Lucas. If you have information please call us," he said.
Police have been inundated with offers of help.
