Some kind of public/private thing I guess. Saw the brown sign directing motorists to it along Ohio SR 48 before the exit at Turtle Creek-Union Road. Went east and it was at the eastern dead end of the road.
The sponsorship signs at the entrance indicate it to be a collaboration between Lebanon City Parks, Ohio Department of Natural Resources, Premier Health, and some other local corporate entities.
It's just some trails and man-made hills for mountain bikes and such to navigate.
The rules list included a prohibition of "unauthorized firearms". The more I see such weasel wording, the less clear it becomes, and the less I care to disarm to (possibly?) comply.
My best guess is that Lebanon maintains it, picks up the trash, etc. The only structure there is an open sided Picnic shelter; one Port-a-let is on site. No worries about either falling into the "government building" prohibition.
Those who haven't paid attention to the vagaries of the Ohio Revised Code might feel compelled to disarm, which is why such rules annoy me. Also, some Gladys Kravitz soccer..bike mom might feel a need to call the po-po if they spot an open, or poorly concealed, carrier.
I have no suggestions towards a solution, as long as our OGA contains Republican "squishies" along with anti-gun Dems, and we have an Attorney General like DeWine.