First, you should update your drivers to the newest version. AMD drivers are usually less stable than NVidia's(believe me, I have experience). Also, you should turn off every application except LoL. Of course, you can turn to overclocking, but that's harder for laptops. Also, you can put Windows Basic instead of Aero. You can turn off explorer.exe, also not that important. You can lower the graphic quality of the game. Good luck!
I did download a driver. I'm not sure though if it was the latest one for my system.