Combine sugar, cornstarch, and salt in the top of a double boiler over simmering water; stir well to prevent clumps. Gradually stir in 5 cups water. Cook, stirring frequently, until mixture is thickened to gravy consistency, 5 to 7 minutes. Remove from heat.

Beat eggs in a bowl until light and foamy. Pour in 1 cup of the sugar mixture gradually, whisking vigorously to avoid curdling eggs. Whisk egg mixture into remaining sugar mixture gradually; return to double boiler. Cook, whisking constantly, until thickened to pudding consistency, 6 to 8 minutes. Whisk lemon juice and butter into pudding gradually. Cool in the refrigerator, 30 minutes to 1 hour.