Allow league through the firewall.
go into your router and enable port forwarding for the correct ports (there's a guide you can google, search "port forwarding & League"
Clean your hardware (maybe your GPU heatsink is clogged and heats up)
Check your processor too while you're at it! How old is your rig? maybe replace thermal paste!
(don't underestimate the effect clogged up heatsinks can have on performance of both GPU and CPU. its mind boggling)
Try to turn off unnecessary background programs. Check your automatic startup folder and see if maybe your system is loaded with stuff you dont need running!
try to play with the ingame settings by turning off shadows, turning down texture quality, etc
whats your computers specs?
GPU, CPU, RAM, HDD/SSD, Case, etc
also, you should turn on v-sync in your gpu software.
unless you have a gaming monitor with more than 60hz refresh, you dont need more than 60fps!
do the bolded stuff first. i guess thats where your issue is!