Make white cake following directions on box. Pour batter into 10-inch greased cake pan, or springform pan, and bake at 350 degrees F for 40 - 45 minutes. Allow cake to cool completely when it comes out of the oven.
Make lemon cream filling by mixing cream cheese and powdered sugar in a medium bowl with an electric mixer until smooth. Mix in lemon juice.
Whip cream in a large bowl with an electric mixer on high speed until it forms stiff peaks. Combine cream cheese mixture whith whipped cream. Stir by hand until blended.
Make crumb topping by combining flour and powdered sugar in a medium bowl. Add butter and dribble in the vanilla extract. Use your hands to mix cold butter into flour and sugar. Break butter into smaller and smaller pieces as you incorporate it into the dry ingredients. Be sure not to press the mixture together. You want to end up with a very crumbly consistency with pieces no bigger than a pea. (If you have trouble making small crumbs, pop the bowl into your fridge for a few minutes.) Chill this crumb topping until you are ready to use it.
When the cake is cool, slice it in half through the middle and remove the top. Spread all but 1/2 cup of the lemon cream mixture onto the bottom half of the cake, then carefully replace the top half of the cake.
Spread the remaining 1/2 cup of cream filling over the top and sides of the cake. Sprinkle the crumb topping on top of the cake and press it onto the sides all the way around the cake.
Now chill the cake for at least 3 hours before your serve it. When you are ready to dig in, slice cake into 12 slices. Serve each slice topped with powdered sugar tapped through a strainer.