I kind of have mixed feelings about all of this.
For starters, muting should absolutely carry over from in-game to the post-game lobby. If you muted someone in-game, you definitely don't care what they have to say (as it's probably going to be very unpleasant anyway.)
That being said, I don't think we should have the ability to mute in the pre-game lobby until there's a dedicated ping/quick chat system set up. In-game you can make accurate calls like objective timers or signaling ganks, but in the pre-game lobby there's just too many things that you miss out on and for that reason it's not a good proposition.
For example, if I wanted to trade with my midlaner (they go ADC, I go midlane) they would have no way of knowing what I'm suggesting. There's no way to suggest what an ally should ban if they're unsure, there's no way to describe strategies, there wouldn't even be a way to ask someone to first-pick your champion. I just think it would be more of a detriment than anything else.
I don't think players should have the ability to view chat logs from the entire game as that just reinforces the mentality of "Look what they said, what I said was justified!" and the like. It shouldn't be a competition of who said the least-toxic thing because people are going to use that as criticism for the punishment system and how they think it doesn't work.