Pete,
In recent versions there are improvements to the backup process that prevent this error, which happens on some hosts.
I recommend doing a manual backup and the upgrading ListMail.
Do you have access to the "PhpMyAdmin" MySQL tool - it's often available in your web hosting control panel.
Instructions for a manual backup using PhpMyAdmin can be found
here.
Please let me know if I can be of further assistance!
Regards