if you post your computer specs we can tell you your problem. The games you listed are really that intense of games as compared to l4d. l4d takes up a lot more proccessing power, ram, and videoproccessing power to run compared to diablo 2.
Without knowing what hardware is in your computer im going to take a guess its a little older, and probably needs a new videocard to run it smoother.
But before we jump to conclusions, lower all your video settings in l4d and see how it runs.
To check your ping and framerate, goto the console by hiting the ~ key. Type in "net_graph 1" without the quotes. If your ping seems high. idk for l4d but if its higher than about 125ms for me i feel lag.
If your framerate(FPS) is not at least 30 in areas with a lot of zombies/people and gunfire, i would suggest lowering your settings because that is your problem.