Preheat the oven to 375°. In a large bowl, gently toss the peaches and blackberries with the granulated sugar and lemon juice. Transfer the fruit to an 8-by-11-inch baking dish.
In a medium bowl, toss the oats with the flour, brown sugar, salt, cinnamon, cardamom and nutmeg. Using your fingertips, mix in the butter until the topping is crumbly. Sprinkle the topping over the fruit and bake for 1 hour, or until the top is golden brown and the fruit is bubbling. Let the crisp cool for at least 30 minutes before serving.
The crisp can be refrigerated overnight. Bring to room temperature or reheat in the oven before serving.
Vanilla ice cream or lightly sweetened whipped cream.