How to fix League of Legends client only opens after the 2-3 minute mark
You should attempt a repair. You can repair the client before you log in.
If this fails you should contact Riot Support by logging into the website with your riot games account and sumbitting a support ticket. Theyw will be able to help you fair better than anyone here.
Your firewall settings might be blocking League of Legends from launching. Or improper DNS settings can cause a problem in your internet connectivity.
Close all the process of LoL, then follow the following instructions:
- Right-click on your Taskbar and click on “Task Manager” from the options.
- In the taskbar, make sure to end the processes named “LoLLauncher.exe”, “LoLClient.exe” and any other process that has "LoL" or "League of Legends" in its name.
- After you have ended all the background processes successfully, launch League of Legends again and check if the error is solved.
Source: https://quaries.com/league-of-legends-not-opening/