Preheat oven to 350° F. Line a 9-inch springform pan or 9x9 square baking pan with parchment paper. If using a square pan, leave an overhang to allow for easy removal of the cake.
Add lemon zest and sugar to a large bowl. Press together with a silicone spatula or wooden spoon to release the lemon oils.
Add in eggs and vanilla, and whisk together for one minute to thicken.
Add vegetable oil, followed by sour cream, and whisk to combine well.
Sift in flour, baking powder, baking soda, and salt and fold in until just combined.
Scrape batter into prepared pan and set aside.
In another bowl or in the bowl of a stand mixer, cream together cream cheese and sugar until smooth. In mixing bowl, mix cream cheese, sugar, egg, and vanilla until well blended. Pour over cake batter in pan.
Mix in egg and vanilla until well combined. Pour mixture over the cake batter in the pan and smooth the top.
Sprinkle blueberries evenly over cream cheese layer.
To make the crumb topping, combine cold butter, sugar, and flour in a bowl. Blend with a fork, pastry cutter, or your hands until the mixture resembles large crumbs. Sprinkle over blueberries.
Bake cake for 45 minutes or until cream cheese filling is set and crumbs on top are golden brown. Allow to cool in pan for about 15 minutes before transferring to a wire rack to cool completely.
For icing, whisk together powdered sugar and lemon juice in a bowl until smooth. If necessary, add a little extra lemon juice to thin out the icing or a little extra powdered sugar to thicken. Drizzle over cooled cake.