[lbarrow]

The responses here are all assuming your grandmothers taxes would go up. But bear in mind LVTs are intend to replace the existing property tax regime (at least in the US). If your grandmother lives in a quiet suburb or rural area, it's likely that her taxes would decrease under an LVT if the LVT was trying to extract roughly the same amount of overall money as a property taxes regime.

If she lives in the middle of a city, then yes her taxes may increase.