There are only two things you care about:
1. How much money does that improvement bring in?
2. How much does that improvement cost?
Neither of those two inputs are affected by a land value tax. Therefore the landlord must reach the same decision, regardless of whether there is an LVT or not, and so LVTs have no effect on whether landlords improve their property.
You might think that they'll be motivated to improve the lot in order to be able to pay the LVT, but that rationally doesn't factor in to the decision to improve the land or not. It only affects the price of the land (Imposing an LVT makes land prices fall by the discounted future cost of the tax).
And not to be rude, but it seems strange to jump into discussions recommending LVTs as a solution to an economic problem without first understanding basic economic theory.