Hi there!
I had some trouble getting Flatpak Lutris to recognize the library from my also Flatpak Steam on an different drive. Maybe this helps out anyone with a similar issue.
Give Lutris access to the Steam Flatpak install and the location of the Steam library. e.g.
~/.var/app/com.valvesoftware.Steam:ro
/mnt/Games/SteamLibrary
I recommend using Flatseal for this step.
Create a symbolic link the steam installation in your home directory
ln -s ~/.var/app/com.valvesoftware.Steam/.steam .steam
Restart both Steam and Lutris. Lutris should now be able to see Steam as an source and launch games using steam.
2 Likes
I’m sorry for the bump, but this was absolutely worth creating an account to thank you for.
I don’t have my Flatpak Steam and Library on a different drive, not even a different path than default, but I still needed to follow your guide to get my Flatpak Steam as a Source in Flatpak Lutris.
THANK YOU 
Thank you for sharing your solution! It’s great that you figured it out, and I’m sure this information will be helpful for others who may be experiencing a similar issue. Here’s a quick summary of the steps you provided:
Give Lutris access to the Steam Flatpak install and the location of the Steam library by using Flatseal to edit the permissions. For example, grant access to the following paths:
~/.var/app/com.valvesoftware.Steam:ro
/mnt/Games/SteamLibrary
Use Flatseal to modify the permissions for Lutris:
Install Flatseal if you haven't already: flatpak install flathub com.github.tchx84.Flatseal
Launch Flatseal and find Lutris in the list of installed applications.
Add the paths mentioned above in the "Filesystem" section under "Other files."
Create a symbolic link for the Steam installation in your home directory:
Run the command: ln -s ~/.var/app/com.valvesoftware.Steam/.steam .steam
Restart both Steam and Lutris.
Lutris should now recognize Steam as a source and be able to launch games using Steam.