Obviously we shouldn't just "turn on" a LVT for land that previously didn't have the tax until now. The idea would be that whenever the government is selling land to private individuals / corporations, instead of setting a property tax of a few % on the land, it sets a land value tax of about 70%. That means that less revenue is made from the immediate sale, but the land will bring in additional revenue over time. So most land would continue to use the original system, while a slowly increasing amount would be "LVT" tagged when it passes through the government's hands. To avoid the "being forced out" situation you describe, there would be a few options:
1. Live in a rural area that is very unlikely to be developed.
2. Make sure to buy a piece of land that is "original system" tagged instead of "LVT" tagged.
3. Buy "property tax increase" insurance. If your land's value goes up, the insurance pays the difference, and you don't notice the cost change.
If those 3 options don't turn out to be sufficient, then probably there's some hacky provision that could be tacked on, like LVT doesn't go up for individuals until they sell their land, or something along those lines. But of course that should only apply to people who are actually living in their own homes, not to landlords.
Anyway, the question is, why go to all this trouble? Why have an LVT at all? The answer is the following: No one created the land. When you're renting from a landlord, some of your rent is for the building, and all the effort the landlord puts into maintaining it. It makes sense that the landlord should be paid for that. Under the current system, though, some of your rent is for the land. That makes a lot less sense. Why pay the landlord for the land, even though the landlord didn't create the land?
Imagine some travellers find an oasis in the desert surrounding a fresh water spring. They (for some reason) decide to settle there, and need to decide how to split up the daily 10 000 gallons of water that the spring produces. I think that probably the travellers would decide to split the water evenly: 100 travellers means that each gets 100 gallons per day. It would be weird if they decided that some of them should be considered "waterlords" and get 2000 gallons per day, and the rest should get 0, and would have to pay the waterlords for their daily water.
Splitting the water evenly wouldn't be communism or anything. If Alice uses her share of the water to grow food, she wouldn't be obliged to share that food with anyone else, since she's the one who laboured to produce it. Everyone still gets to keep or sell whatever they produce, but the spring gushes whether anyone works or not, so the water gets split evenly.
Objection: Maybe some settlers will specialize in farming, and some won't. Obviously the farmers will need to use more water, so shouldn't they get a higher fraction of the water?
Answer: Yes, the farmers will use more water, but they can get it by trading the food they produce with their neighbours in exchange for water to put on their crops. The farmers would essentially be selling their ability to convert water into crops.
Objection: Wouldn't it be an equally good system if instead of trading in water people could trade shares in fractions of the water produced? So 10 000 shares are split equally among all the initial settlers, and each share is worth 1 gallon per day.
Answer: This has a few issues. The main one is that as new people are born and grow up, they would get an equal fraction of the water to everyone else in the "divide up the daily water production" scheme, but they would get nothing in the "divide up the shares" scheme, since all the shares would have been distributed already.