Lutris is an Open Source gaming platform for Linux. It installs and launches games so you can start playing without the hassle of setting up your games. Get your games from GOG, Steam, Battle.net, Origin, Uplay and many other sources running on any Linux powered gaming machine.

Lutris uses community contributed installation scripts to provide an optimal experience and setup. Once installed, games are launched with programs called runners. Those runners include RetroArch, Dosbox, customized Wine versions and many more!

https://lutris.net/

sudo add-apt-repository ppa:lutris-team/lutris
sudo apt update
sudo apt install lutris

To install Epic Games Store on your Linux system, make sure that you have Lutris installed with its pre-requisites Wine and Python 3.
First install Wine and then download Lutris from its website.
https://itsfoss.com/install-latest-wine/
https://lutris.net/downloads/

Installing Epic Games Store

Once the installation of Lutris is successful, simply launch it.

Locale error may pop up when launching from console (and nothing happens launching from GUI). Solution would be to set locale before launching Lutris:
export LC_ALL=C

Note: You’ll have to enter this command every time you launch Lutris. So better to add it to your .bashrc or list of environment variable.

Once that is done, simply launch it and search for “Epic Games Store”. Launch it and log in to your account to get started.
https://lutris.net/games/epic-games-store/