Preheat the oven to 350°F. Grease a 9x13 baking dish or pan with cooking spray, and set it aside.
Whisk together the sugar, cornstarch, and 1 tablespoon of flour in a medium mixing bowl.
In a separate large bowl, toss together the diced strawberries and rhubarb pieces. Add the sugar mixture and lemon juice, and stir until the strawberries and rhubarb are well coated. Spread the mixture into the prepared baking dish.
Add the remaining 1 cup of flour, brown sugar, and oats to a medium or large bowl, and whisk them together. Cut the chilled butter into small cubes, and use your hands to mix the butter into the flour mixture until it is crumbly and all of the butter is well combined. Sprinkle the crumb mixture over the strawberries and rhubarb.
Bake the crisp for 40-45 minutes or until the strawberries start to bubble around the edges and the crisp topping is golden brown on top.
Let the dessert cool for 10-15 minutes before serving. Serve with ice cream, if desired.