Well, this is a case of you are damned if you do and damned if you don't. It opens up a big can of worms if you ask me.
I suspect that King's Island has some type of equipment...be it radar, lightning detection, or computer aided forcasting. Cedar Point and other amusement parks do. The question is, what to do with that information? Beyond shutting down coasters and other tall rides I don't know what would be considered "due care".
If a park were to make a public address announcement that a storm was coming I suspect the odds are far greater that a person would be injured or worse in the insuing panic that would result in people rushing the gates or jamming themselves into indoor areas. I don't know of any park across the country that could accommodate every single visitor inside in the event of a storm. I don't know of any public parks for that matter like baseball/soccer fields that could provide enough shelter. What do they do at a PGA tour event with thousands of people in the gallery?
Let's say the park gave a warning and the people all huddled in a gift shop. If that gift shop was struck by a bolt, caught on fire, and people were hurt would the park then still be held responsible?
It is a sad story but it was an "act of God" and I don't know any company or individual who can control that.