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/ cup strawberry sauce; cool. Cover and refrigerate remaining sauce for serving.
In a mixing bowl, beat cream cheese until light and fluffy. Gradually beat in milk. Add lemon juice; mix well. Add eggs, one at a time, beat on low just until combined. Scraping down bowl after each. Blend in each tablesoon of flour until just mixed, on LOW speed.
Pour half of the cream cheese mixture over crust. Drop half of the reserved 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.
Wrap springform pan in aluminum foil so that the foil comes up all the way to the top edge of the pan. Set cheesecake inside of larger pan that allows for water bath to come up 1 inch on sides of cheesecake pan. Add VERY hot water to come up 1 nch on spring form pan.
Bake at 350 degrees F for 70-80 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.