Stir cornstarch and lemon juice in small bowl until cornstarch dissolves; set aside. Combine Champagne and shallot in fondue pot or heavy medium saucepan; simmer over medium heat 2 minutes. Remove pot from heat. Add all cheeses and stir to combine. Stir in cornstarch mixture. Return fondue pot to medium heat and stir until cheeses are melted and smooth and fondue thickens and boils, about 12 minutes. Season fondue with nutmeg and white pepper. Place over candle or canned heat burner to keep warm. Serve with bread cubes.