If you own the Steam version of Dying Light and you would like to join/invite a friend who plays the Epic Games version of Dying Light, you must:

1. Have an Epic Games account.
2. On https://www.epicgames.com/account/connections, link your Steam account to your Epic Games account.
3. Ensure you have added your friend on your Epic Games account.
4. Start your game session, pause. Now, in the pause menu, press F.
5. At this point, I expect you to see a pop-up saying you have logged into Epic Games.

Your Epic Games friend will show up in the pause menu's friends list. Even in their friends list, you will show up.

When you are online and logged in to Epic Games, it will show them your Steam name. When you're not connected, they'll see your Epic Games name.

If you are an Epic Games player that would like to invite/join a friend who's on Steam, you cannot, unless they have linked an Epic Games account and have logged into Epic Games in-game.

Just ask them to make an Epic Games account if they don't already have one, add it as your friend, then ensure they follow the instructions in the upper section of this page

As an Epic Games player, linking your Steam account is pointless—there is no "log in to Steam" button in the Epic Games version of Dying Light. Consequently, Epic Games players can only see other Epic Games accounts in their friends list.