My experience with Lefty goes back to 2000 when I purchased my Cannondale Super V. One thing I've liked about it how easy it is to 'turn off'. There's a small dial at the top that disengages the suspension - good when transitioning onto solid road riding.
As mentioned above by another post, the center of balance is altered. The implication of which is that it is more difficult to ride 'hands free'.Sometimes I ride hands free with it just to practice my balancing skills.
I seem to remember that the original intent was that lefty offered a longer(higher) range of motion and thus the bike was able to handle more adverse terrain. I'm not sure if that's actually true, but it sounded good at the time.
If you do get one, you'll find it to be a conversation piece. Since it hasn't been widely adopted, I'd imagine that the benefits are not overwhelming.
And one last thing, I've always considered the bike to be "much more of a bike than I am a man".