It sounds like the game is using the Intel graphics. I'd bet on that. Sorry but you'll have to get a LOL user to answer how to make sure it uses the GPU.
As to the 100% disk use, I had that too. Changed the failing HDD to a spiffy SSD to fix that issue.
Hi,
3 days ago I had an issue with my laptop. It started running slow, so I tried a restart, however restarting was not possible due to booting issues. I did a hard reset on the laptop and installed windows again. After adding MS office and Firefox I downloaded League of Legends.
The very moment I got ingame I immediately knew I was unable to play as my FPS rate was averaging at 04 fps. It was hell.
I force repatched, did not help.
I reïnstalled LoL, did not help.
I updated every single driver, did not help.
I set the settings to extremely low, did not help.
Before the booting issue 3 days back, the game was running fine with 60 fps and 13ms.
I noticed that my CPU usage is at 100% when I am ingame, however as soon as I alt+tab to taskmanager f.e. the cpu usage drops from 100% to ~10%.
I also noticed how my disk usage was at 100% for most of the time, but that is solved now.
Some specs:
Lenovo y510p.
Nvidia geforce gt 755m.
8gb Ram.
Intel core i7-4700mq / 2.4 ghz - 3.4 ghz.
Firecuda 1TB sshd.
After trying loads of things I somehow feel my graphics card may be damaged.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic