Combine white sugar, water, lemon juice, and 1/8 teaspoon salt in a thick-bottomed pot; bring to a boil, stirring often. Reduce heat to low, place a cover on the pot, and cook at a simmer for 3 minutes. Remove cover and continue cooking, stirring often, until the sugar and salt dissolve into the liquid, about 3 minutes more. Remove pot from heat and set aside to cool for 5 minutes; pour syrup into a large bowl.
Beat syrup, confectioners' sugar, egg white, and salt together in a bowl until thick, 5 to 10 minutes; add vanilla extract and beat to incorporate, about 1 minute. Add cream cheese to the bowl; beat until smooth.