My understanding is that lightning somewhat originates both up from the ground and down from the sky. As you know, lightning occurs because of the potential difference between the positively charged ground, and the negatively charged clouds. Before a strike, there are both negatively charged "leaders" extending out from the clouds, and positively charged "streamers" from the ground. The streamers stay relatively close the the ground (~50 feet or so) and wait for the leaders to find them. When the leaders connect with a streamer, the electrical path is complete and the large current flows between the cloud and ground. The large amount of heat associated with the enormous current ionizes the surrounding air to create a plasma, which is the light that we see. The result from this immense heat is that the air rapidly expands, leading to compression waves which is the thunder that we hear.

I think lightning is much more complicated than this. I did a search on the web for lightning and found a couple interesting sites.
Below is one. I'm sure there is much more out there.
http://www.exploratorium.edu/ronh/weather/weather.html.
Basically, it seemed that current can flow in either direction because clouds can get charged either positively or negatively compared to the Earth.