Depending on how old Lissie is, she may have gotten married and changed her last name. There are Garnetts in Caroline Co., Spotsy Co., & Stafford Co. Falmouth is in Stafford Co. I have posted a map of the historical plantations in Spotsy Co on the new websitehttp://www.rootsweb.ancestry.com/~vaspotsy/
You could check there to see if there is a Fleetwood plantation shown.
What is the relationship between the Bell family and the Garnett family. It would seem strange that Bell daughters would be allowed to move clear across the country with another family not related?
I'll check around to see what I can found out for you.