Preheat oven to 325 degrees F (165 degrees C). Lightly grease an 8-inch round cake pan and line with parchment paper.
Place cream cheese in a bowl with milk; soak for 20 minutes.
Heat cream cheese with milk and butter in the top of a double boiler over simmering water, stirring frequently, until melted and smooth, about 5 minutes. Remove from heat and cool completely, at least 15 minutes.
Sift cake flour and cornstarch together into a bowl. Sift again into the cream cheese mixture; mix well. Add egg yolks and lemon juice and mix well.
Beat egg whites, cream of tartar, and salt together in a separate bowl using an electric mixer until foamy; add sugar, 2 tablespoons at a time, beating well after each addition. Continue beating on high speed until soft peaks form.
Fold cream cheese mixture into egg white mixture until well mixed; pour into the prepared pan. Place pan inside a larger baking dish and fill the baking dish with water until it reaches halfway up the sides of the cake pan.
Bake in the preheated oven until cheesecake is set and golden brown on top, about 1 hour 10 minutes. Turn off oven and leave cake in oven with door ajar for 1 hour. Transfer to a wire rack to cool completely.
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