In a large bowl combine apricots and cherries. Using a microplane, zest the half the lemon and add the zest to the fruit. Cut the lemon in half and add the juice to the fruit. Add white sugar and cinnamon to fruit. Toss to combine. Set aside.
In a medium bowl combine the brown sugar, flour, salt and cinnamon. Add butter. With your fingers, rub the butter into the flour mixture, working until it resembles wet sand. Add oatmeal and almonds. Toss to combine.
Make a slurry by mixing the cornstarch and water in a small bowl. Set aside. Transfer the fruit to a medium saucepan and heat to boiling, stirring constantly. (You can add a tablespoon or two of water to the fruit if there's not enough juices coming from them). Cook the fruit for 3-5 minutes until the sugar is melted and the fruit has softened slightly. Stir in the cornstarch slurry and bring to a boil. Cook for one minute, stirring constantly. Fruit mixture will thicken.
Transfer the fruit mixture to an 8x8 ceramic baking dish. Sprinkle the streusel topping over the fruit. Bake for 15 minutes, then turn the dish around 180° in the oven. Bake for another 10 minutes until fruit is bubbly and syrupy and topping is evenly browned.
Let the crisp rest for about 10 minutes before scooping into shallow bowls. Serve with ice cream or whipped cream.
Notes
Advantages of arrowroot according to Wikipedia: This starch thickener has several advantages over cornstarch. It has a more neutral flavor, so it's a good thickener for delicately flavored sauces. It also works at a lower temperature, and tolerates acidic ingredients and prolonged cooking better. And while sauces thickened with cornstarch turn into a spongy mess if they're frozen, those made with arrowroot can be frozen and thawed with impunity. The downside is that arrowroot is pricier than cornstarch, and it's not a good thickener for dairy-based sauces, since it turns them slimy.