The six-year-old went missing on Saturday afternoon after he fell into the river while on a fishing trip with his family.
His mother, Kirsty Furze, wrote a touching thank-you note on Facebook to the more than 200 people who joined specialist search and rescue teams.
“I just want to thank each and everyone one of you that I’m so thankful for donations and the food and being out all hours searching for my baby and for the police & rescue and search team.
“I can’t not believe how much my baby has touched all your heart’s he was such a beautiful boy lucas is looking down on everyone saying Thankyou in his own way.
“Lucas will never ever ever be forgotten I’m so over whelmed with the support I have and had and so is Lucas’s dad I really don’t know how else I could show my appreciation to you all.”
“Rest in peace little man gone way to soon. Nanny will look after you I love you much and I’ll cherish the memories forever.
“Life is so important so is family. Cherish the good in life.
“You don’t know what’s round the corner. I little accident is all takes!
“This worlds a cruel place it really is. But I’m so thankful for the thousands of support through the journey of finding my little cousin.
“Took time but we can now say our goodbyes and lets him rest now.”
When Lucas fell into the river, his father and two adults jumped into the water in an attempt to rescue him but he was swept away by a strong current.
Experts from the emergency services used specialist equipment in order to find Lucas, including sonar detectors, underwater cameras, divers, dogs and drones.
Chief Inspector Mark Weller said: "Following the discovery of a body in the River Stour at approximately 9.15am on Wednesday August 21, formal identification has taken place and I can confirm the body is that of missing Lucas.
"It brings an end to our search and I would like to echo Lucas' family's message of thanks to those who came out to help search for him in the last few days. The community support we have witnessed has been heart-warming, even in the most tragic of circumstances.
"I'd also like to recognise the efforts of our partners from Kent Search and Rescue, Kent Fire and Rescue Service, HM Coastguard, the Royal National Lifeboat Institution and all the volunteers who assisted in the search for Lucas.
"While the search may have ended, our support to Lucas' family continues.