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Just knowing the basic concept and not how it is intended to be calculated, this was my reaction:

Thing is... I can only think of two ways to calculate LVT: (a) market value and (b) fixed price per acre.

1. if it's done on the basis of "market value", then it will track real-estate values pretty closely -- I'm not even sure there's a way to disentangle them -- and would therefore have the same problems as PVT as far as gentrification (which is basically what we're dealing with).
2. if it's done as a fixed price per acre, then there's going to be a discrepancy between market value and cost-of-owning -- people who own high-revenue-generating properties in dense areas will be paying the same price per acre as people owning farmland out in the wilderness. Either we'll be passing up huge amounts of revenue from high-density commercial properties, or we'll be driving farmers out of business and forcing families to abandon ancestral homes, or at least break up their property into city-sized lots and sell the rest back to the county (at best).

It turns out that #1 is the actual intent, and the differences between LVT and PVT are seen as positive. I'll need to read more to understand how they address gentrification, however.