This is an ADDON to the base game, that is still Diablo II, you should just add an additional executable to run LOD from Diablo II.
Yes I know, but I would like to catalog all games including physical ones .. not necessarily run it.
The function of adding a game manually would be enough.
You can add another "Diablo 2" (the same you already have), from "Add Games & Friends -> Add game manually", search "Diablo 2" and then click "Mark as Owned"
Now you'll have a "Diablo 2" with two grouped entries (you can switch them right clicking on the thumbnail or clicking on the diamond icon at the top of the game page).
The new one can be linked to the LOD executable.
Unluckily, you can't customize it (like changing images or title), because the appearance of the entry is shared between the two games...
An alternative could be to "Mark as Owned" a random game that you will never get, and them customize its entry entirely, calling it "Diablo II - LOD", changing images and linking it to the LOD executable.
This way you will have two visible separate entries.