Fried Ipswich Clams with Fried Lemons

Name: Fried Ipswich Clams with Fried Lemons
Ingredients: 3 lemons, cut into 1/8-inch thick slices; 1 tablespoon salt; 1 tablespoon sugar; 48 Ipswich or other soft-shell clams (also known as steamers); Peanut oil, for frying; 2 cups all-purpose flour; 1 teaspoon salt; 1/2 teaspoon freshly ground black pepper; 1/4 teaspoon cayenne pepper or to taste; 2 cups buttermilk; 1 recipe Tartar Sauce, recipe follows; 1 large egg yolk; 1 small egg; 1/2 tablespoon fresh lemon juice; 1 tablespoon red wine vinegar; 1/2 tablespoon Dijon mustard; 1/2 teaspoon sugar; Salt and freshly ground black pepper; 1 cup peanut oil; 6 cornichons, finely diced; 1 tablespoon drained capers, finely diced; 1/2 small onion, minced (1/4 cup); 1/2 tablespoon chopped fresh chives