Joe was the name of Lana's grandfather.
Lana was about 24 in the year 2404.
Carey would have been about 72 in the year 2404 (had Janeway not left him to die).
Carey had two sons back home in Ireland.
Lana is the granddaughter of Joe Carey.
The Doctor met Lana at the 9th Anniversary Reunion, even though no one there remembered (or cared) who her grandfather was.