While this article deals in diconnects, you might try some of the suggestions out as they can deal with lag too:
Also, there have been accounts of Flash causing slowness. You might look at disabling Flash in your browser for this site. It is only needed for the videos on the current site version.
Since I have been a Chess.com member, I've played live chess without any issues. But for the last few days, I have had so much lag it is impossible to play on live chess. Every other part of chess.com is working for me and my internet connection does not have any issues. If anyone can help, that would be great.