I'm aware that League of Legends is not currently supported in Crossover, however I decided to try it anyway. I do not get even as far as the launcher--the installer, where you accept the EULA, is solid white and the only displayed icons are the Exit and Minimize buttons. I tried to install some dependencies, including DirectX Runtime - Modern, Visual C++ 2005 Runtime, and Crossover HTML Engine (IE8.0). These dependencies do not seem to alleviate the issue.
It appears that support for LoL may not happen until Crossover uses the Wine 1.3.x base, but we'll see what happens!