If I understand it correctly the squares and the establishments around them are owned by the Morse family. Therefore private property.
If Lady Lake can ban him from city property then he can be banned from the squares as well. Someone who has a history with this guy should approach the powers at be in the Commercial retail group of the villages and get him banned.
As sorry for the guy as you may be, if as reported in the one news article linked in the other posts, he carries a knife, this is a real problem.
Just my opinion,