The liveset points to the performance. But a snapshot of the volume is made and stored with the liveset. That’s a feature: you can adapt the volume in the liveset without actually having to create a copy of the performance.

Changing is easy: go to the liveset screen, press edit and you can see and set the volume of the selected liveset slot. Press exit once you are done.

When you understand the LIVE SET as an ordered set list, then it is easy to understand the “snapshot” of the Volume. Say you need to return to your main Piano sound five or six times during the set. It may appear in multiple slots on the page, now each can be stored with the precise Volume that you need in each instance. Loud in one, not so loud in another...

There is no “one-way” to use the Live Set, but it is designed to be advanced through using an Assignable FS, where each press advances you to the next Performance. In that light, you can understand why the Volume Offset is allowed... specifically to prevent what you thought you needed to do.
You do not have to adjust your original ‘Source Performance’ just to change the volume of the Live Set entry. Each time you use that Performance in a Live Set you can store a different Volume.

If you set the volume of the Live Set to 0 that only affects that particular Live Set entry, it does NOT affect the source data nor any other instance of that Performance whether it is used again hundreds of times. Yes, it’s a feature!

I assume this only works for User Live Sets? I've tried to do this volume edit for the preset Live Sets but the Edit button isn't available for these. Are the preset Live Sets changeable at all by the user - ie can we change which performances are in these Live Sets?

Preset and Library should imply "read only" once loaded. Presets are "loaded" either by factory or your latest firmware upgrade. A library is "loaded" when you install the library. There are no provisions for you to edit either of these these "read-only" areas.

The user area is different - where it's a "scratchpad" area allowing changes to all of the data. Editing, overwriting, and deletion at single objects at a time (Performance, Live Set slot, etc). This memory type used by the User Bank is "read-write" at all times.

The different object types (a Performance - including Audition Phrase, Arpeggio, Motion Sequence, Curves, Live Set, Micro Tuning, Waveforms) can each exist as Presets, Library, or User type memory. You should be familiar with how Performances work under the different memory types. All of the other object types function similarly with respect to how the memory type either allows or does not allow your editing of the data (as described above).

Thus far, all memory types are non-volatile. Meaning - when you turn off or unplug the keyboard - the memory stays put and is not "lost". You do not have to do anything special to ensure your user or preset or library areas are the same when you turn off your keyboard and unplug it vs. leaving the keyboard on.

There are examples of volatile memory in the keyboard. Some examples of these are the edit buffer (changes to your current Performance, motion sequence BEFORE you store/commit the changes), the recall buffer, and the compare buffer. Volatile means memory is not saved if the keyboard is turned off, unplugged, or otherwise put into a mode where the contents of the buffers are changed before saving (like, for the edit buffer, changing to a different Performance without saving the one you're editing).