Clean then hull and quarter the strawberries.
Cook the strawberries with the 2/3 cup of water and sugar in a saucepan over medium heat for 10 minutes or until berries are soft, stirring occasionally Pour off one-third of the sauce into a blender and purée. Return it to saucepan. Mix and stir 1/3 cup of cold water and lemon juice with the cornstarch in a small cup and add to saucepan.
Bring to a boil and cook for 1 minute while stirring. Cool to room temperature. Remove from heat and serve on cheesecke when ready.