In a medium-size bowl toss the cheese with the cornstarch. In a medium-size heavy-bottomed saucepan heat the cider and lemon juice over medium heat until barely simmering. Add the cheese, a handful at a time, stirring until the cheese is melted before adding more. When all the cheese has been added, stir in the salt, cinnamon, nutmeg and pepper to taste. Cook over low heat until thickened about 3 to 5 minutes. Transfer fondue to an enamel or ceramic fondue pot and keep warm over a fondue burner. Serve immediately.
For dipping: Bite-size pieces of cooked chicken or pork sausages, waffle pieces, pizzelles (thin Italian cookies) and strudel, apple wedges and cubes of Cheddar cheese