Combine graham cracker crumbs, sugar and butter. Press onto the bottom of an ungreased 9-in. springform pan. Refrigerate for 30 minutes.
In a blender or food processor, combine strawberries and cornstarch; cover and process until smooth. Pour into a saucepan; bring to a boil. Boil and stir for 2 minutes. Set aside 1/3 cup strawberry sauce; cool. Cover and refrigerate remaining sauce for serving.
In a bowl, beat cream cheese until light and fluffy. Gradually beat in milk. Add lemon juice; mix well. Add eggs, beat on low just until combined. Pour half of the cream cheese mixture over crust. Drop half of the strawberry mixture by 1/2 teaspoonfuls onto cream cheese layer.
Carefully spoon remaining cream cheese mixture over sauce. Drop remaining strawberry sauce by 1/2 teaspoonfuls on top. With a knife, cut through top layer only to swirl strawberry sauce.
Bake at 325° for 55-65 minutes or until center is almost set. Cool on a wire rack for 10 minutes. Carefully run a knife around edge of pan to loosen; cool 1 hour longer. Refrigerate overnight.
Remove side of pan. Thin chilled strawberry sauce with water if desired; serve with cheesecake. Store in the refrigerator. Yield: 12-16 servings.