Line the baked pie crust with hulled strawberries, placed large end down.
For the glaze, crush the remaining 1 cup of strawberries with a fork (or puree in a food processor or blender). Combine the strawberries and sugar in a saucepan. Slowly bring the mixture to a boil over medium heat. Lower the heat and simmer 1 minute.
Mix 3/4 cup cold water with the cornstarch until smooth; gradually add to the hot strawberry mixture. Return to a boil; reduce heat and cook, stirring constantly, until the mixture thickens. Remove from heat. Stir in the lemon juice.
Cool the glaze slightly and spoon over the berries, shaking the pan gently to evenly distribute the glaze. Refrigerate for 2 hours. Top each serving with whipped topping. Serve chilled.