Place a rack in the center of your oven and heat the oven to 375 degrees F. Prepare the topping: In a medium microwave-safe bowl, place the butter and coconut oil. Heat the butter in the microwave for 30 seconds, then continue heating in 15-second bursts, just until the butter and coconut oil melt. Add the oats, flour, baking powder, cinnamon, salt, granulated sugar, coconut sugar, and lemon zest. Stir until clumps form (some will be small and some will be large). Place in the refrigerator while you prepare the filling.
Hull and quarter the strawberries (you will have about 6 cups total), then place them in a large mixing bowl. Add the cornstarch, honey, lemon juice, and vanilla. Stir to combine. Transfer to a 9x9-inch baking dish, including any juices that collect in the bottom of the bowl.
Remove the topping from the refrigerator and scatter it evenly over the strawberries. Bake until the topping is golden brown in places and the fruit is hot and bubbling, about 40 to 50 minutes. Check the topping at the 20-minute mark. If it is browning more quickly than you would like, loosely tent the pan with foil, then continue baking as directed. Remove from the oven and let cool a few minutes. Enjoy warm with a big scoop of vanilla ice cream.
TO USE FROZEN STRAWBERRIES: Thaw the strawberries in the refrigerator overnight or at room temperature for about 2 hours. If they are not yet quartered, do so before adding them to the filling.