Preheat oven to 300 degrees F (150 degrees C). Grease several baking sheets.
Beat the eggs, white sugar, and brown sugar in a bowl until the sugar has dissolved, then beat in lemon juice, almonds, baking powder, cinnamon, ginger, black pepper, allspice, and cloves until thoroughly combined.
Mix in flour to make a sticky dough.
Turn the dough out onto a well-floured work surface, and knead the dough 1 to 2 minutes, adding more flour if needed, to make a smooth, workable dough. Pinch off pieces of dough and roll them into balls about 1 1/2 inches in diameter, and place the balls on the prepared baking sheets at least 1 inch apart.
Bake in the preheated oven until a toothpick inserted into the center of a cookie comes out clean, about 25 minutes.
Remove from sheets immediately to cooling racks to prevent cookies from getting too hard.
Stir together confectioners' sugar and water to make a glaze, and drizzle each cookie while slightly warm with about 1/2 teaspoon, spreading it around the top of the cookie.
