Slice two kiwi into small pieces. Place in ice cube trays and fill with water. Freeze.
Cut remaining kiwi into large pieces; place in a food processor. Cover and process until smooth. Strain; discard pulp. In a 2-qt. pitcher, stir sugar and lemon juice until sugar is dissolved. Stir in kiwi puree. Refrigerate until chilled. Just before serving, stir in carbonated water. Serve over kiwi ice cubes.