First off i recommend you all, if you haven't already, read the short story it was based on titled "Memento Mori" written by Christopher's brother Jonathon Nolan.
Now for starters i do not believe that Lenny has the "condition." I believe that it is mental not physical. My reasoning behind this is that there were many instances where he DID remember things. Throughout the whole movie he would catch glances of his tattoos and have no idea what they were, he would roll up his sleeve, or take off his shirt to investigate, but as he was taking down Teddy's license plate number not only did he remember that he normally gets tattoos but he also remembered what number fact he was on. ALso in the same instance he writes down the 1 and the i exactly the same way, he gets it tattooed exactly the same way, but whenever he read it out loud he differentiated between the two. How could he do this without memory?
Most of the movie will drive you insane to try to figure out, i speak from experience, but the director himself said that there was a logical explanation, unfortunately i don't think we can ever be sure whether we are right or not.
This is my all time favorite movie, so if you have not seen it please do.