Preheat the oven to 350 degrees F.
Combine the butter and sugar for the crust in a bowl. Cut the ingredients together using a pastry blender or two forks. Slowly mix in the flour, forming a dough. Pat the dough out onto a jelly roll pan (about 10x15-inch size). Place the crust in the oven and bake at 350 degrees F until lightly browned, about 15 minutes. Remove the pan from the oven and let cool while preparing the filling.
Combine the sugar, baking powder, and flour for the filling in a bowl. Mix well. Stir in the beaten eggs, lemon juice, and lemon zest and mix until combined. Evenly pour the lemon filling over the baked crust.
Return the jelly roll pan to the oven and bake at 350 degrees F for 15-20 minutes, or until the filling has set.
Remove the lemon squares from the oven and let cool completely. Sprinkle with powdered sugar, then cut into squares or diamonds and store in an airtight container.
