How can I migrate the translated lookup values from one instance of an environment to another?

From the source instance, create an implementation project containing the lookup tasks with the translated values to export them, and then import the package into your target instance. See Export Setup Data Using Implementation Project and Import Setup Data Using Implementation Project. You can use this method to migrate translated values in multiple languages from one instance to another, unlike the methods where you use CSV file packages or manually enter values for setup data using offerings or functional areas.