In a medium saucepan, combine the sugar, cornstarch, lemon juice, salt, and water. Stir well to combine.
Cook the mixture over medium heat, stirring constantly until it thickens and begins to bubble, about 5-7 minutes.
Once thickened, remove from heat and let it cool for about 10 minutes.
Gently fold in the halved strawberries until they are well coated with the sauce.
Pour the strawberry mixture into the pre-baked pie crust, spreading it evenly.
Refrigerate the pie for at least 2 hours to allow it to set properly.
Serve chilled, topped with whipped cream if desired.