Preheat oven to 350 degrees. To prepare the artichokes, place them in a large pot and cover them with cold water. Squeeze the lemons and add the juice and the lemon to the pot and bring to a boil over a high heat. Reduce the heat to medium and cook until they are tender, about 25 minutes. Use the tines of a fork to check for tenderness. Transfer the artichokes to the ice water. When they are cool enough to handle, remove the leaves and the choke (the fine fibrous clump on top of the bottom, in the middle). Trim the edges of the bottoms. Place the artichoke bottoms, eggs and water in a blender or a food processor fitted with a steel blade and blend until creamy. Pour into a mixing bowl and add salt, pepper and flour and combine until pasty. Whip the egg whites in a dry copper or stainless steel bowl until they are creamy and hold stiff peaks. Gently stir into the artichoke mixture. Place a cast iron skillet over a medium high flame and when it is hot, add the oil. Drop dollops (about the size of 2 tablespoons) of batter, a few at a time. When the edges begin to stiffen, turn the pancakes over. Combine the goat cheese and sour cream in a small mixing bowl. Place the pancakes on an oven proof plate and top each one with a large dollop of the goat cheese mixture and place in the oven until the cheese just begins to melt, about 2 minutes.