It is very disappointing that the League of Legends for Mac is closed after 6 Sep. It is really sad to see the compulsory close button after opening the LoL as shown in the below screenshot.
Luckily, there is a way to make the game working again temporary. Technically, as the game is a transplant from Windows with the emulator tool Wine, the whole thing is just running a Windows program in Mac environment. Therefore it is possible to put the files of LoL in Windows back to Mac to trick the server that I am using Windows. Of course, please take your own risk to do the following steps. =]
Step 1: Download the Windows version of LoLLauncher.exe here.
Step 2: Replace the LoLLauncher.exe with the downloaded one under
/Applications/League of Legends.app/