The resort's manmade lake, Seven Seas Lagoon, had "no swimming" signs at the time, but none that warned of alligators.
"Melissa and I are broken," father Matt Graves wrote in a statement released Wednesday. "We will forever struggle to comprehend why this happened to our sweet baby, Lane.
"As each day passes, the pain gets worse, but we truly appreciate the outpouring of sympathy and warm sentiments we have received from around the world."
"We will solely be focused on the future health of our family and will not be pursuing a lawsuit against Disney," the statement said.
The statement also said Graves' parents, Matt and Melissa Graves, were establishing the Lane Thomas Foundation in their son's honor.
"We know we can never have Lane back, and therefore, we intend to keep his spirit alive through (the foundation)," it said. "It is our hope that through the foundation we will be able to share with others the unimaginable love Lane etched in our hearts."
The family asked for privacy, "as we focus on our family."
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