In my town there are several lots that have the tag "open to visitors". I know that such lots can't be bought and I think it's unfair. This universal type of lots is very convenient, because in its place can be built anything, plus there is never pandemonium. I'd like to know if there is a way including local and third party mods that will allow me to unlock this type of lot to buy.

The lot type was originally intended for lots that have a rabbithole plus other things that might (somewhat) draw a sim in or keep them on the lot after they are finished with rabbithole business. Such as a school that has a playground off to the side. Our sims cannot own municipal lots like schools, libraries, and City Hall but I didn't realize there was a block on purchasing any lot with that lot type. Perhaps I've been missing something and there is a reason for this.

I'm not going to and never was going to buy a city hall, a police station, or anything like that. Yes, they belong to the state, as it should be. To tell the truth, I changed the type of some lots myself. Up until a certain point, it was a meeting place, and, you know, this decision from the developers led to strange situations. The characters gathered outside and... stood there. Sometimes they could go inside the empty room, get their musical instruments and start playing. It looked like an underground party. So I decided that the store (which includes shelves and cash registers) should have the tag "open to visitors" (or "closed to visitors" if there is nothing inside yet). Now I decided to start my own business and noticed this problem. If there is no solution, then... What can I do? I can only choose some other type of lot, which to some extent is suitable for this.

Just like the No Visitors lots it's a generic lot that has no business or residential value. They also tend to be good spots for sims with the Loner trait to hangout on as sims will rarely visit those lots unless a rabbithole is on it. I have 2 cabins in my town one with Visitors and one with No Visitors the sims that frequent those lot's the most are Loners.
It's possible those lots also serve to provide Loner sims a place to get away from other sims.

I usually use the "closed to visitors" tag for lots that don't have anything the characters can use. However, lots "open to visitors" seem to me very profitable because of its versatility. I once saw a mod that allowed players to buy rabbit holes that can't be bought. So I had an assumption that there would be something for my situation as well.

Back when the game first came out and could still be that way if you just use the Base Game not sure though that lot was more of draw for sims but as time went on and more and more lot types came out it became less and less viable as the advertisement attraction was shifted to those new lots. I never seen anything that could change that so it's probably in the scripting.