Bake the pie crust according to the package instructions or as directed in the recipe. (See Notes for baking a homemade pie crust.) Let the crust cool completely before making the filling.
Cut the strawberries in half. Reserve half of the strawberries in a large bowl and set aside.
Add the remaining strawberries to a medium saucepan along with the sugar, ¼ cup water, and lemon juice. Stir to combine. Mash the strawberries with a fork or potato masher until chunky, then place the pot over medium heat and bring the mixture to a boil, stirring occasionally.
Once the mixture comes to a boil, reduce the heat to medium-low. Dissolve the cornstarch with the remaining ¼ cup of water in a small bowl, and stir it into the pot. Simmer, stirring frequently, until translucent and thickened, about 5 minutes. Remove from the heat and let cool for 10 minutes.
Pour the filling over the strawberries in the bowl and stir to coat well. Pour the filling into the baked crust, and gently move the strawberries around, and jiggle the crust to make sure the filling reaches the bottom and there are no gaps. Smooth the top with a spatula.
Chill the pie, uncovered, for at least 3 hours or until set. Slice and serve with whipped cream, if desired.
