Preheat oven to 350°F Lightly grease a 9×13-inch baking pan (or use the Baker’s Edge pan, if you have one).
Begin by making the crust.
In a large bowl, cream together 1/4c sugar and 1/2c butter, until smooth and fluffy. Working at a low speed, gradually beat in 1 1/2c flour and 1/4t salt until mixture is crumbly. Pour into prepared pan and press into an even layer. Bake for about 17 minutes, until set at the edges.
While the crust bakes, prepare the filling.
In the bowl of a food processor, combine lemon juice, lemon zest, strawberry puree, sugar and eggs and process until smooth. Add in flour, baking powder and salt, then pulse until smooth.
Gently pour the filling over the hot crust when it has finished baking. Return pan to oven and bake for 23-26 minutes, until the filling is set (There will be a light colored “crust” on top from the sugar in the custard - nothing to worry about).
Cool completely before slicing and use a damp knife to ensure clean slices.
Store bars in the refrigerator, especially on a hot day.