No. Four of the five Great Lakes are binational (U.S.–Canada):
Lake Michigan lies entirely within the U.S. (bordering Michigan, Indiana, Illinois, Wisconsin). However, it is hydrologically one lake with Lake Huron (connected by the Straits of Mackinac), and its water levels, quality, and fisheries are managed jointly under the Great Lakes Water Quality Agreement and the International Joint Commission.
So while Lake Michigan is geographically wholly U.S., it is governed as a shared resource. No Great Lake is unilaterally "owned."