At some point he was introduced to the newly downloaded Donna Noble, by Doctor Moon. They fell in love and got married, having a simulated son Josh and simulated daughter Ella.
Lee and Donna lost each other while being rescued from the computer, Donna's last words to him being a promise that she would one day find him. Donna was led to believe that Lee wasn't a real human. It turned out that he was a human after all, but since he had a stuttering problem, he couldn't call out to her when she left with the Tenth Doctor.
"Lee" was apparently not his real name, as Donna determined that no one with that name was in the Library when the Vashta Nerada attacked. (TV: Forest of the Dead)
Behind the scenes
In the DVD writer commentary on The End of Time, Russell T Davies says that the writers toyed with the idea of bringing Lee back as Donna's fiancé, but it wouldn't really have made sense.
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