What do you want changed in ?

Add tournament brackets and keep eliminating people if they lose until someone gets first place.

I mean... it would be awesome if that happened, and if someone is absent after joining the tournament, they will automatically lose if they don't come by the end of round 1 (by the time everybody completed all round 1 games).

Lichess Team Playoffs.
Have country chess federation team events.
Top ten players from each chess federation, having chess playoffs.

Lichess is the best site for playing chess online.

In my opinion, the platform has one big flaw: it invests too many resources to promote Arena tournaments.
This is not bad in itself. The problem is that this competition system instills certain habits that conflict with the principles of good chess. (I'll leave out the arguments that support my statement so as not to lengthen this post)

Fortunately, a few days ago, Lichess took a decisive step towards perfection: Lichess included Swiss tournaments in her offer.
But Lichess still needs to take an extra step to reach fullness: implement Round Robin tournaments.
Apparently, the developers of Lichess are not willing (or able) to take this final step.
But if they did, Lichess would be the most complete platform because it would have:

1- Arena tournaments for the crowds,
2- Swiss Tournaments for the large teams, and
3 - Round Robin tournaments for small teams.

Less emphasis on item 1 to free up the resources needed to make item 3 a reality: That's what I would change in Lichess!

It would be nice if you follow the FIDE-rules:
1. You can't be flagged if your opponent has insufficient material to force mate, eg lone bishop or knight or two knights.

2. Your opponent can't reject a draw offer under condition 1.

These are not FIDE rules.
As long as mate is theoretically possible (even if bad play is required) you can be flagged.

Lichess BOT tournaments for BOTs exclusively. They should add BOT tournament points.

Make an option where you can restart your lichess rating (350 rating deviation), but you must start at 1000, as a penalty...

I can't believe no one has yet asked for this in this topic once it has been asked so many times.
I would love to have the possibility to search my own games for particular openings and positions. This could simply done, I believe, by adding the option "my own games" beside the "masters" and "lichess" on the options of opening explorer tool.
Pleeeeeaaaase do this. It is so important.
As a coach I would also love to see implemented the option to search a specific player's game by opening or position. Again, I think just adding a fourth option in the opening explorer tool called something like "search player". This of course may lead to privacy issues but one could have the option not to have games searched by third parties or none friends or something like that.

I urge you to implement this! :)

Here are the things I think should be changed:

1. When a player reports a cheater with a game supplied, he should be refunded no matter what. Last time I reported someone who played tons of bullet games after my game with him, so by the time my report was reviewed, he was way above 40 games since he played against me and I wasn't refunded. Not a fair system.
2. I would love to see the spectators' chat in the lichess TV page itself.
3. I would love to see 2 separate chats in the broadcasts page, one for players who want to exchange thoughts of their own without engine assessments and the other one for the rest who love to write "stockfish says +2.3" etc. But I know it's too much to ask.

Bughouse would be a welcome addition. Not that I ever play it or want to play it, but I love watching bughouse games. :)