For the shrimp croquettes: Melt the butter in a medium skillet over medium-high heat. Add the shallot and saute until softened, about 4 minutes. Use a wire whisk to stir in the flour. Cook for 1 minute, and then add the shrimp. Stir in the milk and cook until the mixture is very thick, stirring constantly for 1 minute. Remove from the heat and add the lemon juice and some salt and pepper.
Allow the croquette mixture to cool completely before shaping into small meatball-sized balls. Place the breadcrumbs in a shallow dish. Mix the beaten eggs with 2 tablespoons water. Double coat the croquettes by rolling them first in the crumbs, then in the egg mixture, and then in the crumbs again. Place each coated croquette on a baking sheet. Cover the croquettes and set them aside
Heat the oil to about 375 degrees F in a deep, heavy pot. Preheat the oven to 150 degrees F.
Add the croquettes to the hot oil in batches, making sure not to crowd the pan. Cook until golden brown, about 3 minutes. Drain the croquettes on paper towels, sprinkle with salt, and keep warm in the oven as you fry the remaining croquettes. Make sure the oil returns to 375 degrees F before cooking the next batch, or they will be heavy and greasy.
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