Leemon, MissouriLeemon is an unincorporated community in Cape Girardeau County, in the U.S. state of Missouri.The community is on Missouri Route 177 approximately three miles east of Fruitland.HistoryA post office called Leemon was established in 1875, and remained in operation until 1905. The community was named after Leemon Haile, the proprietor of a local sawmill.