electric mixer, beat butter and 1/3 cup sugar on medium speed 1 minute. Sift together flour and cornstarch. Add to butter. Blend until dough is soft, about 1 minute. Drop by teaspoonfuls onto ungreased baking sheet. Bake until very lightly browned, about 15 minutes. Transfer cookies to racks to cool.
Meanwhile, combine 2 1/2 cups sugar, melted butter, and lemon juice. While cookies are still warm, mound 1/2 teaspoon icing on each; icing will melt. Cool cookies completely.
