In a medium saucepan, whisk together sugar, eggs, lemon zest, cornstarch, and salt until smooth. Add lemon juice, whisking until smooth. Cook over medium-low heat, stirring constantly, until mixture is bubbling, thickened, holds shape of whisk, and registers 170°F (76°C) on an instant-read thermometer, about 7 minutes.

Strain mixture through a fine-mesh sieve into a medium heatproof bowl. Add butter, 1 cube at a time, stirring until combined and mixture is smooth after each addition. Cover with a piece of plastic wrap, pressing wrap directly onto surface of curd to prevent a skin from forming. Let cool completely. Refrigerate in an airtight container for up to 1 week.