Lutris, dependences not satisfied

[ActionParsnip]

sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 2F7F0DA5FD5B64B9
sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 76F1A20FF987672F
sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys C5E224500C1289C0

You haven't added the keys to say they are "OK". It's just a warning but cleaning up takes seconds.

[mastablasta]

add PPA then:

sudo apt update
sudo apt upgrade
sudo apt install lutris

[Impavidus]

The result is :

Reading package lists... Done
Building dependency tree       
Reading state information... Done
Package python3-magic is not available, but is referred to by another package.
This may mean that the package is missing, has been obsoleted, or
is only available from another source

That shouldn't happen. python3-magic is available from the main focal repository. On my system:

$ apt-cache policy python3-magic
python3-magic:
  Installed: (none)
  Candidate: 2:0.4.15-3
  Version table:
     2:0.4.15-3 500
        500 http://nl.archive.ubuntu.com/ubuntu focal/main amd64 Packages
        500 http://nl.archive.ubuntu.com/ubuntu focal/main i386 Packages

Check your /etc/apt/sources.list. It must mention focal main. Maybe refreshing software lists helps. sudo apt update should do that, but it can fail if some timestamps are wrong. First deleting the lists will force apt update to download them again. The lists are in /var/lib/apt/lists/.
Your output from sudo apt update shows the main focal repository on the first line as "Hit". This means that no changes were reported compared to the version cached on your system, so it didn't redownload.

The only other possibility I see is a server problem. In that case, switch to a different mirror.

[dunivixs]

I have solved the problem :
I just went to this site : https://ubuntuplace.info/questions/3...es-apres-avoir

I ticked this : "Conical-supported free and open-source software (main)

I did this commands :

sudo apt-get clean
sudo apt-get autoclean
sudo apt -f install
sudo dpkg --configure -a
sudo apt-get -f install
sudo apt-get -u dist-upgrade

Then I unticked some ppa unused

And I tried to install lutris and this works !!

Thanks for everyone

[ActionParsnip]

Looks like you didn't import the key as per the guide linked earlier (https://linuxconfig.org/install-lutr...al-fossa-linux)

wget -nc https://dl.winehq.org/wine-builds/winehq.key
sudo apt-key add winehq.key