Preheat the oven to 350°F. Make the brown sugar-oatmeal topping: Combine oats, flour, brown sugar, cinnamon, and mayonnaise in a medium bowl. Squeeze the mixture to create large clumps. Set aside.
Combine peaches, blackberries, lemon, sugar, and cornstarch in a large bowl. Transfer the peach filling to a large ovenproof skillet or 2-quart baking dish. Top evenly with the brown sugar-oatmeal topping.
Bake the crisp at 350°F for 35 to 40 minutes, until the topping is golden brown and the fruit mixture is bubbly. Remove from the oven and serve warm with a scoop of ice cream, if desired.