I'm using Hardy (server) on quite a few machines and I'd like to upgrade to the latest LTS. Is it safe to edit my
sources.list file to just point to the new LTS, or should I do a succession of dist upgrades until I reach the latest LTS?
No. You should never just edit
sources.list. Use the update-manager, or if you use command line, use
do-release-upgrade. You can upgrade safely from LTS editions to other LTS editions, or otherwise, you need to step via each release. Only those pathways are supported, and prevent some issues that can otherwise occur with improper upgrades.
I believe you can upgrade directly from LTS to LTS, see e.g. https://help.ubuntu.com/community/LucidUpgrades