Lee's story begins at the onset. Society hasn't even fallen everywhere yet considering lee was cheated on, had a trial, and was being brought to jail. The walker that was crossing the road randomly and then lee killing the zombified cop was like one of the first incidents both characters even heard/saw of walkers. And lee's story in episode 1 all happens while rick is still in a coma.
The webisodes, and michome's story also take place around this time, when people still are living their daily lives and aren't aware of walkers until you see them randomly eating people on the streets.