None of what you wrote make it ok for anyone to have their dog off of a leash there.
Also, it's not 'not really a dog park', It's precisely NOT a dog park and there are signs all around the lake stating to keep all dogs on leashes.
Please refer to the flow chart if you are still not sure if it's ok or not.
There are too many other people around there trying to enjoy other activities. It's quite possibly the worst park in the entire city to have your dog off off of a leash due to sheer number of people that pass through that area. FYI, I watched a dog run down a biker, knock her down and bite her at Antrim. So sorry for being a little passionate about this, but it really gets under my skin. Also, I'm not a dog hater by any means. I love dogs, but I hate their owners sometimes.