Is the US Army Corps of Engineers land not a part of my city?

I live in a town in Texas that banks a lake the US Army Corps of Engineers own. My property however backs up to the lake where we are required by our city to fence at a certain elevation due to the dams spillway level. The corps have always owned this land as well for a base where the lake now covers. The lake has been here before the town, I'm almost positive, when the corps flooded it. The level that is required however is almost never reached by the lakes water level as that is its peak and leaves a decent amount of land that is owned by the corps, making it ineligible to consider it our property. The lake spans over the course of near a dozen or more cities across in our area. Since this is spread all throughout as government property, does the extra amount of land belong to my city? I mean the lake can't really be divided into sections as city properties and is only policed by Texas and Federal Game Warden. The shoreline could be measured into the city boundary lines, but at what point does the fluctuating water level due to inconsistent precipitation/temperatures no longer surpass the line?