Meanwhile, start prepping the tomato mozzarella mixture. First dice the onion. Set aside.
Then cut the zucchini - if they have a thick skin, peel, but if they’re on the smaller side feel free not to peel. Cut in half lengthwise. Then cut both of these halves in half lengthwise. Cut the 4 pieces into 1/2 inch chunks. Set aside.
Place the tomatoes in a large bowl. Cut the fresh mozzarella into approximately 1/2 inch chunks. Add to the bowl with the tomatoes. Dice the basil. Add to the large bowl.
Heat a large nonstick skillet over medium heat. Add the butter and then the onion. Saute for about 3 minutes, stirring occasionally. Then add the zucchini and saute for another 5 minutes.
While the mixture is cooking, add the Parmesan, lemon juice, flour, sugar, and salt to the large bowl. Mix well together.
When the onions and zucchini are done, add to the bowl and mix well. Put in the refrigerator for about 10 minutes.
While the mixture is cooling, take out the pie crust. Sprinkle flour onto the work surface and roll the pie crust into an approximately 11-inch circle. Gently fold in half and then in half again and transfer to a 10-inch pie plate. Open up the folds and pour the tomato zucchini filling into the crust. Fold the sides over the filling, overlapping when needed. Refrigerate until cold, about 10 minutes.
Preheat oven to 375 degrees. Bake pie on a rimmed baking sheet until the crust is golden brown, about 45 minutes. Allow to cool for 15 minutes before serving.