I have two questions about the game clients and running games via Lutris.
I have installed the blizzard client through Lutris and it works fine. When I setup Hearthstone through Lutris, it wants to setup a new install of the blizzard client. Even if I cancel out of it and point it to where the original blizzard app is installed it still does not work.
I have the same issue with Steam. I installed steam and then installed Civ5. I want to launch Civ 5 from Lutris, however, it also wants to install its own version of Steam.
Regarding Blizzard games: Install the new client and put hearthstone on a separate partition/disk/directory. You can start the old client afterwards and point it to the Hearthstone directory (“Search games” menu).
Never put your Blizzard games into the battlenet directory because you have to thow away and reinstall the client from time to time anyway and you want to keep your games untouched.
Right now, you will just have to live with multiple blizzard apps installed. It does no harm since they are in their own prefix. Just start hearthstone when you want to play hearthstone. That prefix contains fixes to make the game run.
The standalone blizzard app installer is just that, and not really suited to run all games. Some games work without modifications, but others do not. So it is just to run Blizzard App.