Is it a recent problem, or has LoL always been this way on your PC? If the former, & you've installed any updates recently (driver, Windows, etc.), try rolling them back. If it's the latter, then it might be an issue with your CPU. Although you only need a single-core CPU to run the game, the minimum is a 2.0GHz CPU (3.0GHz recommended), & yours is barely above that. You're OK on RAM & your GPU, so any issues are probably more CPU-related.
Unfortunately, there's not much room for improvement on your CPU. Your board is not one of the "AM2+/AM3" boards, & based on the list of supported CPUs (https://www.asus.com/Motherboards/M2NXE/HelpDesk_CPU/) you're already really close to the top. The absolute best CPU available, the X4 9850, is only rated at 2.5GHz (maybe 14% faster), so I don't know how much it will actually improve your situation. And you're still talking about replacing a 9-year-old CPU with another 9-year-old CPU (both of which are vastly inferior to even the 1st-generation Core i3/i5/i7 CPUs). What you may need to do is just plan on saving up some money to upgrade your system -- something like a Kaby Lake i3/i5 or a Ryzen CPU (or even the Ryzen APUs) would be more than sufficient.