In a medium bowl, combine the cheeses and cornstarch and toss to coat evenly. Set aside.
In a heavy medium saucepan, melt the butter over medium heat.
Add the mushrooms and cook, stirring, until golden brown and most of their liquid has evaporated, about 5 minutes.
Add the shallots and cook, stirring, until soft, about 1 minute.
Add the cider, water, and lemon juice, and bring to a simmer.
Reduce the heat to medium-low and add the cheese-cornstarch mixture in 3 additions, stirring constantly and adding more cheese as the previous addition has melted.
Once all the cheese has been added, add the pepper and salt and stir.
Remove the pan from the heat.
Carefully pour the fondue into a fondue pot for serving, being sure to follow the manufacturer's instructions.
Serve hot with dipping items of choice.
YIELD: 2 cups, serving 4 to 6