Request A Lot Cleaning
If there is a lot in your neighborhood that is dirty, you can send a request that the NYC Department of Sanitation come out to clean it by filling out an online form. You can also call 311.
NYC Sanitation will clean public or private lots; they will also clean the lot whether or not it has a fence around it.
You might want to make a request for a lot cleaning when you start organizing your lot - a lot clean up will send a clear signal to the neighborhood about your intentions.
If your lot is already part of the GreenThumb program, you will need to make any lot cleaning requests through your contact at GreenThumb.