Customer is unable to delete the Lightbox collection, the delete feature doesn’t show up. They are able to delete all other collections besides this one.
AEM as a Cloud Service - Assets
Lightbox is a special type of collection that provides easy access to assets and is assigned per user. It is the “add to favorite” feature for your DAM (Digital Asset Management). Every user has an exclusive Lightbox that is automatically created when the user logs in to Adobe Experience Manager (AEM) Assets and serves as the user’s personal image gallery.
Although Lightbox resembles a collection, you can’t perform all the actions that you normally perform on collections. For example, you can’t delete, share or view settings for a Lightbox. In addition, you can’t add it to other collections. However, you can edit the assets inside a lightbox.
You can find more info about this special collection here 1.