LVT taxing the empty lot next door at the same rate as a multimillion dollar hotel is exactly what makes it so efficiency enhancing because it give land owners economic incentives to use their land productively rather than just holding it and waiting for it to appreciate in value. With LVT, prices would exclude the value of the land.
LVT can be combined with other policies and taxes. You have to look at the whole package of policies to determine progressivity. LVT+UBI is progressive