I have been faced with this issue as well. It shouldn't ruin the friendship as long as you both are mature and can communicate. By the time I got my friends interested in league I had grinded to lvl 30 alone. I'm assuming your friend isn't a level 30 yet?
If he is and he is still feeding that's a different problem you must approach. On the other hand if he is still going through the grind of getting to 30 and wants to play with you. Consider persuading him to play some bot matches and offer to even play with him. You are sacrificing your normal play time to still play together and he is should hopefully be learning new strategies as you guys dominate AI together.
Explain to your friend the concept of feeding and how to avoid it. He doesn't have to kill the other champions to succeed in a lane. Which means not dying is a victory in itself. I would also suggest wat%%%%% some videos together with commentary on how to improve your play.
Well hope this helps and at least its a starting point.