Grab the battle.net installer from the lutris website, optionally extend it with the D4 installer (it just creates a second shortcut using the same battle.net install you just did).
Once bnet is installed, you can add Lutris games as shortcuts in steam (you may need to do it from desktop mode without steam running) by right clicking on games and clicking add to steam.
From there you just need to install D4 in the bnet client and away you go.
I personally used Lutris:
Grab the battle.net installer from the lutris website, optionally extend it with the D4 installer (it just creates a second shortcut using the same battle.net install you just did).
Once bnet is installed, you can add Lutris games as shortcuts in steam (you may need to do it from desktop mode without steam running) by right clicking on games and clicking add to steam.
From there you just need to install D4 in the bnet client and away you go.