Game issues

Ok, I'm not entirely sure if this is in the right section but I have tried to play two games consistently today and both times I have been repeatedly crashed out of the game (one of them required me to entirely restart my laptop because I could not force the game to close and try to re-load into the game). I know my laptop ain't anything flashy but it meets League of Legends base requirements, but for some random reason, my Graphics Card repeatedly slows me to 1 to 2 frames per seconds, sometimes mid-trade, and it results in me just being forced out of the game and has landed me multiple LeaverBuster penalties as a result, making it difficult to play with people because the moment they see that penalty they just stop the Que and kick me from the party which just upsets me to no end. I don't know if this is a client issue or a computer hardware issue, but to give some perspective, I play the game at the absolute lowest settings (30 fps, capped and very low graphics quality). Any tips on this?