FPS Dropped to zero in game

So i tried to log in the league client but it was taking awhile for the authorizing process so i decided to close the client and try again. When i tried again the client wouldn't open, it showed the league logo but nothing happened, this happened twice. I then decided to restart my computer and log in again. I was authorized quickly and i was in the client.

i joined a game with my friend and everything was fine until the 15-10 minute mark. At this point, my fps was slowly decreasing through the rest of the game. When i first downloaded league (2 weeks ago) i was able to play at 115 fps i, however, capped my game at 60 to and i play at all low setting to keep the game running smoothly. My fps went from 60-50 to 50-40 then made its way to 40-30 then it went to 20-10 then eventually i was running less then 10fps before my game turned black (i was still abl to see hud and shop) but i was at 0 fps and i couldn't move or do anything. I even got an afk warning and i was stuck like this until the end of the game.

When i hit the 20-10 fps mark i checked my task manager and everything looked fine. My cpu was running at 40-60% which it usually does and nothing was out of the ordinary. I really want to fix this so i can play games and not get another afk restriction (i have got one in the past due my client not running the game past champ select multiple times in a row)