He slipped into a weir near Tutbury Mill at about 18:00 BST on Friday.
The fire and ambulance services were called shortly afterwards and he was pulled from the water, but died at Queen’s Hospital in Burton-upon-Trent.
His family said: “We are heartbroken and devastated at the loss of our vibrant, happy, bubbly little man”.
Kai, known as “Ginge”, had an older brother and sister.
In a statement issued by police, Kai’s family called him “our ray of sunshine who brightened up the darkest day.
“He was always out and about, whether it was fishing, taking his beloved dogs for a walk with his dad or just in the village.
“He would smile and put his thumb up to everyone.”
Kai’s death is not being treated as suspicious.
FRIENDS and family of tragic schoolboy Kai Lambe held a lantern tributeon the 24th of August to the Hatton nine-year-old.
Kai died in hospital after falling into a weir on the River Dove at Tutbury on Friday.
His family and neighbours in Hatton decided launching flying lanterns into the night sky would be a fitting tribute. The lanterns and orange balloons were released into the sky at the spot where he fell and floating tealights were lit on the water.
Organiser Sophie Sanders said: “I wanted to get all of us together in memory of Kai.”
More details: www.watersafetymap.co.uk/map/details/219
“Weir on River Dove, Staffordshire” by www.flickr.com/photos/paul_blakeman, license: creativecommons.org/licenses/by-nc-sa/2.0