In a medium bowl, toss the cheeses with the cornstarch to coat.
In a heavy medium saucepan, melt the butter over medium heat. Add the shallots and cook, stirring, until soft, 1 minute. Add the cider, water, and lemon juice and bring to a simmer. Reduce the heat to medium-low and add the coated cheese in 3 additions, stirring constantly and adding more cheese as the previous addition has melted. Once all the cheese has been added, add the salt and pepper and stir.
Remove from the heat and carefully pour into a fondue pot for serving, and following the manufacturer's instructions.
Serve hot with dipping items of choice.
