Actually, none of the Shawnee National Forest is privately owned. And, it is owned by the Federal Government not the State, so i find it hard to believe that any of it gets leased out by the State.
I beg to differ, at least about some of it not being privately owned. While picking up a plat map at the National Forest Service headquarters in Harrisburg an official told me that not all of the available public hunting land was marked as sometimes signs are weathered or torn down. On the plat map I bought (which shows all of Shawnee in Illinois) there is quite a bit of the forest itself which has been private property for many years. They advised me to pick out an area or two I was interested in and buy maps for those specific areas detailing the boundaries.