permission denied mkdir /Volumes

There are access control restrictions on that directory. You can inspect those from the command line:

ls -lOe /

(That's a capital letter O and not a zero 0) I would suggest mounting your volume to another directory - either /tmp or $TMPDIR rather than messing with the restrictions that are designed to prevent what you have - an actual directory with actual files in /Volumes.

Without knowing your script and workflow, it's hard to guess/advise other than not changing things that Apple will change back next time you patch the system.

Your vendor of the LTO tapes should have software to handle mounting the volume in a manner that uses Apple's disk arbitration framework so you don't have to manage the mounts in a script.

You could add a user to have explicit write access in that directory if you're certain that's what will help:

sudo chmod +a "User 1:allow:add_subdirectory" /Volumes

The default permissions of the directory /Volumes are:

...
drwxrwxrwt@  4 root      admin  hidden  136 Apr 22 22:05 .
 0: group:everyone deny add_file,add_subdirectory,directory_inherit,only_inherit
...

I suggest to repair permissions either with Disk Utility/diskutil or a 3rd-party tool and/or modify the permissions manually.