Whether you need to bring the fish in or not would depend on how cold it gets in your area. It looks like you have a half barrel and that might not provide enough protection if you get below freezing weather.

As far as the lily goes, if it is a tropical lily it will need to come inside, but a hardy lily can stay outside. You will want to cut it down to the pot as the weather gets colder. Rotting plant material isn't good for the fish.

If it was your first year, maybe the lily wasn't mature enough to bloom. Also if it doesn't get enough sun it might not bloom. The other plants should probably be removed. They look like the type that might die in cold weather.

It is true, you do not want to let the barrel ice over. You want at least a small hole for gas exchange. But don't pound on the ice if it does form. That can damage the fish. Sit a pot of hot water on the ice (holding on to it) to let the heat melt the ice.

I am not in Ohio so I can't give you precise information, but I would err on the side of caution with that small a pond.

You can't let the lily roots freeze even if it is a hardy lily.