Sometimes you might run into a document library or a list that doesn’t have a delete option under the list settings, this is common for default lists like Documents.
Those library’s cannot be deleted because they have a property called AllowDeletion set to false.
In order to delete those library’s you can use the following power shell script which set the AllowDeletion property to true.
$web = Get-SPWeb(“http://YourSite”)
$list = $web.Lists[“Documents”]
$list.AllowDeletion = $true