For sauce, in a large skillet cook fresh sweet peppers and garlic in hot oil over medium heat about 20 minutes, stirring occasionally. (Or, if using peppers from a jar, in a 2-quart saucepan cook garlic in oil for 30 to 60 seconds or until light brown. Stir in peppers; remove from heat.)
Place the pepper-garlic mixture in a blender container or food processor bowl. Cover; blend or process until very smooth. Add the 1/2 cup water, the basil, tomato paste, vinegar, sugar, salt, and black pepper. Cover and blend or process with several on-off turns until basil is just chopped and mixture is nearly smooth. Transfer to a 1-quart saucepan. Cook and stir sauce over medium heat until heated through.
Meanwhile, measure thickness of fish. In a large skillet bring the 1/4 cup water and half of the lemon slices just to boiling. Carefully add fish. Return just to boiling; reduce heat. Cover and simmer until fish flakes easily when tested with a fork. (Allow 4 to 6 minutes per 1/2-inch thickness for fresh fish; 6 to 9 minutes per 1/2-inch thickness for frozen fish.) Remove fish from skillet.
To serve, spoon some of the sauce onto 4 dinner plates. Place a fillet on top of sauce on each plate. Garnish with remaining lemon slices and, if desired, basil. Freeze any remaining sauce for another time. Makes 4 servings.