Preheat oven to 375 F.
In a 2 1/2- to 3-quart non-reactive, stove-top and oven-proof casserole thoroughly stir together the sugar, cornstarch and cinnamon. Stir in the berries and fruit, orange juice and butter until smoothly incorporated. Bring the mixture to a simmer over medium-high heat. Continue simmering, stirring frequently, just until the mixture thickens slightly and clears, about 2 minutes. Taste and add lemon juice, if desired. Set aside.
For dough: In a food processor, combine the flour, sugar, baking powder, soda and salt. Pulse several times to mix ingredients. Add the butter and oil to flour mixture. Process in on/off pluses until the fat is cut in and mixture resembles coarse crumbs. (Alternatively, place the ingredients in a bowl. Cut the fat into the flour using forks until mixture resembles coarse crumbs.)
Turn out the flour mixture into medium-sized bowl. Add 1/3 cup milk, tossing with a fork just until evenly incorporated. If necessary, stirring very lightly, gradually add enough more milk to form cohesive, but not wet dough. Let the dough stand a minute or two. Knead and shape it with flour-dusted hands into a smooth mass.
Pat the dough into a 3-4 inch discup Lay between sheets of wax paper. Press or roll out into a round 1/4-inch smaller than the interior of the casserole used. Peel off one sheet of paper. Center the dough, paper-side up, over the fruit mixture. Peel off and discard the second sheet. Cut some decorative slashes in the dough top for heat vents. Garnish the dough by sprinkling with 1 tablespoon sugar, if desired.
Bake on the center oven rack for 35 to 40 minutes or until the top is nicely browned and a toothpick inserted in the dough center comes out clean. Let cool at least 10 minutes and preferably 20 minutes before serving. Garnish servings with ice cream, if desired.
Keeps, covered, at room temperature for 36 hours, and then refrigerated for up to 3 days longer. Reheat the refrigerated cobbler in a low oven or let stand until room temperature before serving.