This question is out of the scope of land value taxation. The overall tax burden would fall on the institution running the condo (HOA/company/whatever). How they decide whom to charge and how much, etc. would be a separate question government by different rules and laws.

Which is not to say that the outcome would be fair, but whether it is or not would depend upon how these organizations are regulated and run.

I don't think it is out of scope though because wether the government or your HOA/whatever is deciding how to appropriate the LVT is at the whims of someone else. I'm mostly for LVT but it gets supper messy with multiple ownership properties on land.

Also, LVT don't fix zoning as the value of your land is based on what you can make from it. If your land is zoned for only single floor parking, nobody is going to buy it for more than they can earn through single floor parking so the land won't be that valuable thus it won't have a high land value tax.

Why would they pay the same rate? From my understanding, the condo corporation would receive the tax bill. It would then be up to them to determine how they should charge the individual units.

Do people on the lower floors pay for lift maintenance?

Generally speaking no. When there needs to be major maintenance, each condo unit owner pays N% of the cost where N% is defined as your ownership stake (also your voting weight) in the condo. N is roughly your unit's square footage / the sum of every unit's square footage.