In the Steam client, when you hover your mouse over the Library button the dropdpw options are SteamOS + Linux, Games, Software, VR, Tools and so on.
I think Lutris should add something like this. The default sorting will be your games. But to add a Software and/or a Tools section were you can add game related tools and software such as Steam, Origin, Epic Game Store, Antimicro, Discord, Mumble, Dolphin, PCSX2. This way you will have a section that will only show your games and another section for software to manage games and gaming related things. I can add Steam or Origin into Lutris but it is considered a game when it is software, not a game.