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.
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.