Yes. There is a "strip" of land around each reservoir that is owned by the city. The amount of land owned varies with the reservoir because of when they were built, and how property was acquired. Generally, there is a 25-foot strip around Lake Whitehurst and Little Creek Reservoir, and a 10-foot strip around Lake Smith. Even with erosion, Norfolk still owns the property around the reservoirs.
For Lakes Lawson, Prince, Western Branch, and Burnt Mills, the amount varies. Check your property plat for an indication of what Norfolk owns. A professional survey may be required to determine the exact amount of property owned by the City of Norfolk.