In a small saucepan, stir together the berries, sugar, cornstarch, and lemon juice. Cook this mixture over medium-high heat, stirring frequently, until it becomes very thick and jammy. This should take about 5-10 minutes. Transfer the mixture to a heat-safe bowl, and cover with plastic wrap. Chill in the freezer while you make the cake batter.
Preheat your oven to 350 degrees, and generously grease an 8 inch square or round cake pan. Line with parchment paper if desired, and set aside.
In a large bowl, beat together the butter, sugar, sour cream, and lemon zest until combined. Add in both eggs and lemon juice, and beat to combine- the mixture may be lumpy- that's okay! Add in the flour, baking powder, and salt, and beat until fully incorporated. The batter will be very thick.
Spread a little more than half of the batter into the bottom of your prepared pan. Evenly spread the cooled jam mixture on top of this layer of batter. Place the remaining batter on top in dollops all over to make spreading easier. It will likely be a bit messy, but that's okay- spread the top layer of batter as best you can.
In a small bowl, use a fork to combine all the ingredients until a crumb forms. If the mixture is too wet, add another tablespoon of flour. If it's too dry, add one more tablespoon of melted butter. Sprinkle the crumbs evenly over the top of the cake batter.
Bake the cake for 50-55 minutes, or until a cake tester comes out clean and the top has reached a deep golden brown. This is a long bake time, but the jam slows things down- don't worry! Cool completely in the pan before slicing and serving!