This isn’t at all challenging. Unless there is a by-laws providing exclusive use and conditions for ownership attached, this is all common property. This discussion has been dragging on for months if not years, now. Your neighbour is out of line and you need to stop this nonsense right now.
Apply to Fair Trading for a mediation (Form HERE) under section 138 on the basis that you want a CTTT order telling your neighbour that they can’t make changes to the lift shaft or any other part of common property without Owners Corporation permission and you want an order clarifying that the lift shaft is, indeed, common property.
Gather together the original strata plan, which will define common property, as a well as any other documentation and bring this matter to a head.
The fact that the neighbour is the only person using the lift shaft makes no difference to its status as common property. Just as an example, external stairs to a property’s front door are only used by its residents but they will be common property, at least in part because of the implications their maintenance and repair have on the integrity of the rest for the building.
Readers who are not aware of this long-running saga can find previous postings below.