Preheat the oven to 350F. Grease a 9x13-inch glass baking dish with non-stick cooking spray.
In a medium mixing bowl, whisk together the flour, baking soda, baking powder, and salt. Set aside.
In a large mixing bowl, with an electric mixer beat together the butter and granulated sugar until light and fluffy. Beat in the eggs and vanilla extract.
With an electric mixer, mix in the lemon zest, fresh lemon juice, half of the flour mixture, and half of the sour cream. One well combined, add the remaining half of the flour and sour cream and mix well.
Reserve 1 1/2 cups of the cake batter. Pour the rest of the batter into the prepared 9x13-inch baking dish and spread out evenly. Dollop the cream cheese filling all over the cake batter and use a knife or offset spatula to gently spread the cream cheese out as evenly as possible. Pour the reserved cake batter over top of the cream cheese layer and spread out evenly.
Sprinkle the crumble topping over the cake.
Bake at 350F for 30-35 minutes until a cake tester inserted into the center of the cake comes out clean.
Cool the cake in the pan completely to room temperature. Dust the top of the cake with powdered sugar. Cut and serve.