Problem is that a lot of games take more space than they say they will. Some games will allocate more than necessary due to how compressing works, images, textures, etc. You can run league on a flash drive, but it won't be a fun experience. You could run it on an external hard drive that has decent specs, but on surface I wouldn't be personally interested in opening it up to connect an external for faster speed (USB is cringe).

You could just run Windirstat to see what is filling up your hard drive. Then run CCleaner and try to remove what you don't actually need. There's a lot of random cache/excess data a lot of programs keep around (ie chrome), which can easily be alone in excess of 10-20 GB lol