You can assign them to any of the fields suggested here already. You can also create your own custom field name if you wish such as WRITER.
However keep in mind that most library management programs and players only support the display of the typically "standard" fields. As such any data like this that gets saved into your music files is only going to be useful in very few places, like mp3tag.
@Hypersky75 Or do you ask how to get the metadata from Discogs ("Lyrics by" and "Music by") into the Metadata Album in the upper right corner of Mp3tag - as result of the used Websource Script?