Where is lee memorial health? Lee Memorial Hospital Contact Phone Number is : 239-343-2000. and Address is 2776 Cleveland Avenue, Fort Myers, Florida 33901, United States. Lee Memorial Hospital is a more than 350 beds, Level II Trauma Center in Florida State and was opened in 1916.What is the lee memorial health system? Lee Memorial Health System, a century-old institution that has used the “Lee Memorial” brand for most of its history, could soon change its name to “Lee Health” in an effort to emphasize its non-hospital offerings.