The pilot of the special light sport amphibian airplane stated that he had planned a local personal sightseeing flight, which included departing from an airport, landing on a lake about 20 miles away, then returning to the departure airport. During the approach to landing on the lake, the pilot left the landing gear in the extended position, which was the wrong position for a water landing. Once the airplane touched down on water, it decelerated quickly, nosed over and came to rest inverted. The pilot added that there were no preimpact mechanical malfunctions with the airplane. When the airplane was recovered from the lake, substantial damage was observed on both wings and the fuselage. The landing gear was observed in the extended position and the landing gear selector was also in the landing gear extended position.