Sit down with him and identify why he is toxic and getting more toxic.
Is the end of the season coming close and he is trying to hit his season goals and thinks that every win counts? Let him understand that seasonal goals are a long term goal and if he is good enough, he'll climb to his desired goals. However, if he is struggling to get to his goals and relying on luck, then that is not the true definition of being there.
Does he just want to win every game? Riot matchmaking gives both teams equal chances to win based on the current MMR (not to be confused with true MMR) of the players in game. So let him know that the expectation to win every game is unrealistic.
Let him know that it's a video game, and you are there to have fun. It's OK to mess up things mechanically, even pros mess that up. If it's outplays, see if you can review the VODs and replays with him and see if you can come to an understanding on why that gank messed up. BTW, laner's positioning matters when it comes to a successful gank. If he doesn't know that or how to execute on it, then I can probably dig up some old videos and on how to do that.
Relavent video from a Pro player & sports psycologist standpoint. 5:00-9:35 is probably where you'd want to listen to, though the whole thing is a pretty good listen as well.
https://youtu.be/VBCb4-VNDNk?t=5m