Double round-robin

Double round-robin tournaments would be nice to have : Opponents would meet twice during the tournament, alternating the colors.

Good Idea!

Sounds good in theory. But what happens when players who are having a bad tourney withdraw? (Which happens a lot).

Withdrawals in OTB tourneys are discouraged by sanctions (e.g. the removal of prize money or not inviting such a player next year).

But what would we do on Lichess? Imagine a 6 person double round robin with 10 rounds. What happens if someone withdraws after 8 rounds. Are all their games null and void? Only second half games (rounds 6,7 & 8)? And it could affect the tourney outcome.

If I had previously beaten the withdrawing player and the result is voided...I suffer. But if the withdrawing player had beaten me...I prosper. Neither of which seems fair to me.

My experience in a real Double round robin tournament was when one player withdraw, the other obtained the point. The game wasn't voided or null. The philosophy of the tournaments in this places was the same: each player should be responsible and participate in every game. But, not all players do it, and some ones suffer for other who wasn't play 5 games and one day came to play the 6.
For me, the organizasers are resposible for this: rules and behavior of players. And if I wan to win or be champion, I have to obtain the most points or win all the games. Not more, not less.

Maybe it would work best for private tournaments.
Maybe a computer-generated player could sit in where a player dropped off and just to make things a bit fair, the computer player should have the same rating as the original player.
A reconnect could hurt the private tournament. There does not seem to be a way to reconnect to private tournaments. Especially when players are on the same server that lost the connection.

"the computer player should have the same rating as the original player"
Easier said then done. Trust me.