Lake Lawtonka, itself, is owned by the
City of Lawton. http://www.cityof.lawton.ok.us/parksnrec/lawtonka.htm
It's my understanding Lawtonka's the oldest lake in Oklahoma with the original dam being completed in 1905. The dam has been added onto (more accurately, atop of) several times over the years and was built with taxpayer money. The lake was built mainly as a water supply for the City of Lawton and secondly for recreation. Lawtonka is still the main water supply for the City of Lawton with the city water treatment plant located just below the dam. City of Lawton (public) property - hence City of Lawton police jurisdiction.
Lawtonka is predominately a watersports lake and so I never cared for it mostly for that reason. I'm sure many a fishermen can relate to having witnessed many a watersportsmen that didn't care much, if at all, about whether they're disturbing the fishing or not.
Lake Ellsworth is also owned by the City of Lawton and was built as an additional/backup water supply and for recreation. Swimming/skiing were not allowed until a few years back but the motorized type of watersports is restricted to a small area relatively close to the dam. Due to the murky waters and the restricted area at Ellsworth you don't get many watersports problems while you're there.
Other than limitations of laws/regulations or possibly not having any applicable licenses and permits (which goes to same), Lake Lawtonka
IS open to the general public and anybody can use it for recreational purposes of their choosing.
Unfortunately, the way I am I would've struggled with not using a lot of profanities while I was telling him where he could shove it and probably would've lost that struggle!