Hello LoL community.
The following is an alternative method for getting LoL working through a proxy to that provided in this thread:
Whilst the instructions in the above thread work, this approach is much more simple and elegant: it doesn't require using a third party application like proxifier or proxycap, which, being proprietary software, may not be entirely trustworthy. Nor does it require access to an additional external proxy (for example, with Your Freedom), which will usually make the launcher much slower. As such, I think this method will be much better for the majority of users.
The method below is for use in Windows 7, and consists of defining an enviroment variable called "all_proxy" (without the quotes). For older versions of Windows, this procedure should still work, but you will have to Google how to set enviroment variables under that older version.
NOTE: setting the all_proxy variable will, in theory, make all programs use this variable to start up, so it may also fix many other games with connection problems. However, not all progrms will actually use the variable at all, and these will be unaffected.
1. Right click on My Computer, and select properties.
2. Click "Advanced system settings" in the sidebar
3. Under the "Advanced" tab, click "Environment variables"
4. There are 2 types of environment variable. If you want to set up the proxy as a systemwide variable (for all users), make click "New" under "System variables". Otherwise, create it under "User variables for $USERNAME", where $USERNAME is, well, your username...
5. Type "all_proxy" (again, without the quotes) as the variable name, and then your proxy address in the form "$HOSTNAME:$PORT", where $HOSTNAME is the hostname or IP of the proxy and $PORT is the port through which you want to connect. You should know these: they depend on the proxy you are using.
6. Hit OK, OK and OK!
Feel free to ask any questions if you have trouble, I will try to help, to the best of my abilities. If you do ask, please do provide enough information about what doesn't work though! Neither I or anyone else will be able to help otherwise.