Preheat oven to 375°F. Coat a 7-by-11-inch glass or ceramic baking dish with cooking spray.
Stir together mulberries and cider in a large bowl; let stand for 10 minutes. Add apples, lemon juice, cinnamon, 3 tablespoons sugar, and 1/4 teaspoon salt.
Stir together oats, flour, chia seeds, and remaining 1 1/2 tablespoons sugar and 1/4 teaspoon salt in a separate bowl. Using 2 knives or a pastry blender, cut butter into mixture until it resembles coarse sand. Stir in walnuts.
Scrape apple mixture into prepared baking dish. Top with oat mixture. Bake until well browned and bubbly, 30 to 35 minutes. Serve warm or at room temperature with yogurt, if desired.