I will give you some tips on how to increase your fps in lol...it's tips that i have found on internet from a lot of sources and from my experience and compile them all together.

First open up the menu while in game (esc) then go to video settings.

- Second, make sure you have Vertical Sync unchecked.
- Then set your Frame Rate Cap to Benchmark or High.
(use the one that gives you the most fps. Both options will give you higher fps then the stock option Stable).

You can see your FPS meter in the upper right corner.
You should always aim for an FPS over 30FPS - Make sure you don't get to much fps drop in intensive teamfights.
60FPS + is very good!

Other method is that you can use some programms like GameBooster to maximize your pc performance but i don't reccomended so much because it's such a little difference.

Why would you uncheck V.Sync?
The only time you need V-sync is if you get screen tearing or if you allready have an stable 60+FPS with everything maxed out.... V-sync will decrease your FPS alot and as you said will limit the fps to the update frequency of your monitor.

By disabling V-sync you will get a really good FPS increase.

A quick example:
I could only play LoL on very low/shadow off with around 25fps while having v-sync on.
After turning it off I could play at all medium settings with around 45fps.

+Fps_lol