sure, some vacant lots are city owned. This is often true in blighted parts of towns/cities, because they were taken over for lack of property tax payment, decades ago. Like where I'm at, for instance, there's a particularly blighted portion of our city (skid row), where apparently decades ago, it just didn't pay for persons to think they could use it for any commercial purpose. Thus when buildings burned or got perpetually abandoned by the heirs, some actually went unpaid on property taxes, because the owners were simply left with no other economic choice. These become weed-choked vacant lots, with short-cut trails across them, homeless encampments, litter, etc... I would not hesitate to hunt those (if I felt the need, but obviously, they are .... by definition .... junk strewn).
Others might still be owned by someone, somewhere, albeit hundreds of miles away. Example: One time a building was torn down in this skid-row section I allude to in the above paragraph. We did fairly good during the demolition process (tokens, v nickels, barbers, etc...). And since we were there anyhow, we continued to "cave in" the soil at the lot which adjoins this one, and continued to find a spread of targets going one direction. However, we were aware that we were actually going into the next property with the bobcat tractor we were using to scrape off the top few inches (to get below the junk). So I researched through the assessor's office, to find out who owned that land beyond they invisible line in the land. Turns out it was someone hundreds of miles away. So we sent them a nice letter asking if we could have permission to scrape off all the weeds, at our own cost. Ie.: "clean it up" if we could, in doing so, take the top few inches of weeds, trash, etc... with us, at our cost (obviously, point being, so we could detect and be below the top few inches). We never got a response, so we gave up.
Now here it is, years later, and I sometimes pass by that lot. It is still there, still abandoned, still weed-choked with abandoned shopping carts, homeless camp tents, etc... A part of me thinks I could simply have done it, and no one would ever have cared less. But did you want the technical answer, or the realistic one?

(or .... put another way.... do you think the homeless folk who cross through, or camp there, have asked permission?

)