I think the problem is that your behavior was continual, it's just that this particular game was the trigger that finally got you permad. You must have a history of negative behavior, and you may have been repeatedly banned and never reformed.
Hence, this particular game was the final straw as far as the reporting system goes and you were banned for telling someone to off themselves. I kinda agree with riot, and your buddy can't help you. The fact of the matter is that this isn't the first instance that you were toxic in a game. Although this particular game was the trigger for your ban, you overall deserve it because of your continual bad behavior.
I'm sure both you and your buddy are both aware of particular times you were temporarily banned or chat restricted, and are probably also aware that you just waited out your ban while joking about it and not reforming. Also, you may have even temporarily made an extra account to pass the time.
Luckily, your buddy still has a chance to learn from your own missteps and reform his own behavior before also being lumped with you and getting perma-banned.
I'm sorry to say that riot finally deemed that your behavior made you finally eligible for a perma-ban.
And this means that Riot officially decided that they don't want you, in particular, playing their game. Unfortunately and quite frankly, it seems you are the type of player they don't want playing this game because you continually contributed to a toxic environment.