Let me tell ya a story
One game I queued up with my boyfriend to play, and we got put with a trio. All was going well until we started losing. That's when the trio decided to gang up on us, and it was awful. I had them muted after a while but my bf kept them unmuted to see what they were saying.
When we got to post game chat, that's when the worst started.
They first tried to get the other team to report us, so we had to say "we weren't doing anything, we had them muted because they were harassing us and cursing up a storm"
Then they started spamming the same curse word over and over again so the entire chat was filled with '****'
Then they started saying they wouldn't get in trouble, you can't report for cursing. Filling up the whole chat with filthy language, making fun of me, telling us we were bad players, etc. This was at 1 in the morning, I was tired and fed up and pretty upset. I won't lie, that was probably the worst toxicity I've seen in my 2 years so far.
So I came to the boards and asked "If you have screenshot proof and the people were incredibly toxic, can you report through a ticket so these people can't do it to anyone else before the system kicks in and finally punishes them?
An arbiter came in and told me how to do it, and I sent Riot a nice long ticket explaining the whole situation and including screenshots. I encouraged them to look at in game and post game chat logs, and told them that these people used their numbers advantage (2v3) to harass me and my boyfriend and I was not confident that they would be punished and didn't want this happening to anyone else. I also included that this was my worst gaming experience so far, and apologized for any spelling mistakes seeing as it was 1 am and I was tired.
A day later I get a reply saying that they would look into it, however they cannot tell me what happened to the players. I am almost certain they got punished.
Post game chat is free game, however anything REALLY serious like death threats, and like what you mentioned above, I would definitely take screenshots and send them a ticket. Saying you are going to murder someone is SERIOUS, and I have no doubt that Riot would take immediate action against that person.
Hell I even heard a story a long time ago of a kid making death threats in game and someone reported it with screenshots and the police showed up at the kids house.