In a zip-top plastic bag, combine cheese and cornstarch; mixing well to coat cheese. Set aside. In a saucepan, heat cider, wine and lemon juice until mixture begins to simmer. Add reserved cheese about 1 cup at a time; whisking until cheese is melted before adding more cheese. Repeat. Stir in nutmeg and pepper.
Transfer to fondue pot; keep over low flame, stirring often.
Serve with bread cubes, steamed veggies or fruit wedges.