POA dues charged by lot or unit?

I can't speak to Texas law, but how dues are assessed are generally defined in the governing documents for the association, not state or local law. Those would be the CCRs (aka Declaration, Deed Restrictions), bylaws, or any other documents that govern your association. These documents form a contract between the owners and define the association and the rules it is run by.

Our subdivision originally had 2 types or levels of owners. Homeowners and vacant lot owners both had same voting power but 2 classes. Once you recieve your certificate of occupancy you are required to pay full dues, prior to that, it was a reduced amount. The attorney that "restated" our articles and bylaws was an idiot. He changed it to where you are not required to pay any assessments until the CO is issued by the county. So all the vacant lot owners do not have to pay dues according to the amended HOA bylaws and rules. Read your documents carefully and look at the wording of said documents. A vacant lot owner obviously does not use the amenities as a homeowner would, they should have 2 classes of dues or assessments. Lot owners should not have to pay more than 50% of full HOA assessments in my opinion. If they are making you, then something is wrong with HOA management company and legal council.