Is the lag you're seeing due to FPS drop or latency increase? I'm not sure how much bandwidth streaming takes but that may be the issue. I've been running 2 23" monitors with my old GTX 460 without any problems.
As for a dual card setup goes, you might see a performance increase if FPS is your issue, but I don't have first hand experience with 2 cards in one system.
That sounds like an issue I was having a week ago. I would play WoW, or GW2, or any other MMO in fullscreen and play a movie or show in vlc, and wmp and it would lag my second monitor. If that sounds like your issue, I fixed it by overclocking my CPU.