The info I have about the children of Hercules Agee (1799-1857, son of Noah) and Jennetta Hill has been gathered from several other researchers and the 1850 census. The only child I find listed with them who would be called "Lizzie" is Sarah Elizabeth Agee, b. 22 Oct 1830, Clarke, AL, who married Jackson Raley b. 1827 MS. Lizzie and Jackson are found in the 1850-1880 censuses and do not appear to have had children. They lived in Marengo, AL, in all of these, except for 1870 census when they were found in Cold Bath, Clark, AR (honest!).
BTW, there are several Hercules Agees. I descend from the one who was the brother of Noah Agee (grandfather to Sarah Elizabeth Agee, mentioned here).
I'm very interested in all Agee info, so would be glad to help research your "Lizzie Agee," if she does not appear to be the same as the one I spoke of above. Can you tell me anything more about her....who she married, etc.?