The only city I can guess that would be the "Lion City" and relevant to Gainesville or Florida is St. Augustine, FL. Lions guard a bridge there, and I've heard from a few people that it has occasionally been referred to as the "Lion City" because of it, but it's better known for other things, so it doesn't really come up.
Born, raised, and still live in Florida.
The only city I can guess that would be the "Lion City" and relevant to Gainesville or Florida is St. Augustine, FL. Lions guard a bridge there, and I've heard from a few people that it has occasionally been referred to as the "Lion City" because of it, but it's better known for other things, so it doesn't really come up.