Process cheese, sour cream, mayonnaise, lemon juice, salt and pepper in food processor until combined. Remove 3/4 cup to small bowl. Add basil to remaining sauce in processor; process until sauce is smooth. To each sauce, stir in 2 tablespoons water to thin slightly. Refrigerate until serving.
In shallow dish or pie plate, lightly beat eggs and milk with fork until blended. On sheet of wax paper, combine bread crumbs, garlic salt and cayenne.
Line a baking sheet with foil. Toss ravioli with beaten egg gently to coat. Remove a few ravioli at a time, letting excess drip off. Coat ravioli in crumb mixture, shaking off excess. Place on prepared pan; repeat process.
Over medium-high heat, heat oil in 5-quart saucepan until 350°F on deep-fat fry thermometer. Fry a third of the ravioli at a time, turning occasionally until golden brown, about 2 to 3 minutes for each batch. Drain on paper towels. Serve with Dipping Sauce. (Or refrigerate, then reheat in 500°F oven for 1 to 2 minutes.)