"the anniversary of my arrival by barrel at Esgaroth on the Long Lake"
This is a reference to an episode in The Hobbit
when Bilbo freed the captive dwarves from the wood elves. The dwarves then hid in some empty barrels that were to be dropped into the river. Clinging to one of the barrels, Bilbo travelled with them down the river to the Long Lake, arriving at Esgaroth, a town of men on the lake. Here the dwarves emerged from their barrels and were welcomed by the townsfolk, before finally resuming their mission to the Lonely Mountain and the dragon Smaug.