I find it a bit irritating that the rating displayed in correspondence games is always stuck at what it was when the game began, and is never updated to include recent events.
I think it's done this way because the rating change will be calculated from the two players' starting ratings. I. e. if you start a game as a 1500 vs a 1800, once the game ends the rating changes are calculated from these two numbers, regardless of whether in the meantime you've become a 1700 and your opponent has become a 1600. So displaying updated ratings in the game window could lead to confusing situations (e. g. in the example above, if the game was drawn, it would show you as a 1700 gaining rating from a 1600).
Maybe lichess could display both the rating at which the game was started as well as the updated rating (in brackets or so); but showing two values might be confusing as well.
Personally, I think it's fine the way it is. Remember that you can always see the updated rating by hovering your cursor over a player's name.
