Bring sugar, cornstarch, salt, and warm water to a boil in a medium saucepan set over high heat, whisking constantly. Cook, whisking constantly, until mixture thickens, about 5 minutes more.
Stir in butter and lemon zest and juice. Cook, whisking, until smooth, 2 to 3 minutes more. Remove from heat; transfer to a medium bowl to cool completely before putting into jars. Sauce can be refrigerated up to 2 weeks.