By default Mail::Box tries to create a /var/mail/username.lock file and you don't have the permissions required to do that. You can set lock_file to something else, but you need to know what locking your MTA is using or you might loose mail.

One thing you can do is Move the mail file to your home directory. Make sure the move is atomic. That will also solve your delete problem, as the MTA will recreate the mailbox nextime you get mail.