Rub inside of fondue pot with cut garlic clove. Place pot on stove, pour in chicken broth and lemon juice, and cook over medium heat until bubbly.
Turn heat to low, and gradually stir in cheeses with a wooden spoon. Blend in cornstarch, and continue to cook, stirring constantly.
In about 2-3 minutes, mixture should be thick and smooth (do not allow fondue to boil.) Season with salt and pepper and nutmeg. Place fondue pot on it''s stand at the table, without the burner. Serve with bread cubes and apple slices.