A subset of speed chess/blitz chess. The difference is that lightning chess is played with time controls that do not exceed 2 minutes per person per game and which is often 1 minute.
Lightning chess is frantic and involves (what seems like) mental reflexes more than thinking. A minute for the entire game does not leave much time for thinking very hard about anything at all. If you don't feel that you know the position, you're probably going to lose.
Play lightning chess online. Check out http://lightningchess.webjump.com/