It's no coincidence that people who support LVTs are typically YIMBYs -- we want to reform urban planning and land use to make it easier to build things.
An LVT gives no such incentives. LVT is explicitly agnostic about how the land is being used. You pay the same, no matter how the land is being used. That's why it's economically efficient.
However, a conventional property tax (and also income tax and capital gains tax etc) disincentivise developing. An LVT can help raise enough revenue to be able to lower or eliminate those other taxes, and thus indirectly help remove disincentives to developing.
So under property taxes, the parking lot owner can afford to wait and have the lot sit empty; under an LVT, they have an incentive to develop.
The LVT has no influence on building.
If you draw a two-by-two matrix where the columns are property tax yes/no and the rows are LVT yes/no, you will find that the rows have no influence at all, and it's all about which column you are in.