That doesn't make a difference to how land value tax works. If a landlord doesn't own the land, he leases it from someone who does.
But to make LVT simpler to understand (and economically equivalent): you can imagine the government owns all the land, and rents out plots for eg 20 years at a time to the highest bidder. To help people plan better, the auctions can be done 5 years ahead of time. So leases for 2036 - 2056 will be auctioned off in 2031.
You can stagger the auctions, so a few leases get auctioned off every week.
If we step away from the realms of imagination, then in the UK typical leaseholds are legally valid for about 100 years, with some going up to 999 years. Of course, many leaseholders - the rent seeking Landlords - may come and go within those lease cycles.
Or are you proposing State confiscation and management of the land? I can’t quite tell from your post.
I was describing a simpler system for implementing UBI. You are right that I left out how to transition to that system.
For example, you could do more or less the same thing that the UK did to abolish slavery: buy out all the existing land owners / lease holders.
I suggested 20 years as a reasonable time frame for leases. In principle, 100 years might would also work. 999 years is probably far too long.
Now, instead of auctioning off the leases, you can also have individuals officially owning the land, but instead you tax them a certain fraction of the market value of the land every year. Economically that's equivalent.
A 999 year lease is basically economically the same as owning the land. So you should more or less treat it the same.
In the last place I rented (London), the private landlords were unlikely to own the land. Fixed term leasehold was overwhelming common, not freehold.