Combine blueberries, orange juice, and sugar in a medium saucepan. Cover and gradually bring to a boil over medium-high heat, stirring occasionally. Reduce heat; simmer 4 minutes.
While berries cook, combine the lemon juice and cornstarch in a small bowl. When the berries have simmered for 4 minutes, stir in the cornstarch mixture. Boil 1 full minute, stirring often to prevent sauce from spattering. Remove from heat. (If not using sauce immediately, cool, transfer to a storage container, and refrigerate up to 4 days).