I dont't see why it should lag with the i5... Maybe u have bad internet and u think its the game. But if ur sure its the game not internet, then yes u need to upgrade ur graphics and maybe one more GB for RAM
You are definitely being hampered by the GPU. Definitely a 58xx series will do you wonders. Even a 57xx series card is better than what you currently have.
I had a 3870 which was great for awhile, but definitely, it hampered me when I upgraded to an Athlon II X3 720 from my Athlon64 X2 4200+.
3850 wasn't even a good card when it came out...far too weak for any serious gaming. And 2GB really isn't enough these days; 4GB is considered the bare minimum. GPU is by far the bigger concern though...