Download the latest release of overwatch.dxvk-cache
The location for placing the file will depend on whether you used the lutris script to install battle.net or overwatch 1. If you use a custom path, change accordingly.
If you use the overwatch 1 script:
~/Games/overwatch
If you use the battle.net script:
~/Games/battlenet
If you already start the game and have the dxvk-cache file you just need to replace the old one with the previously downloaded one.
In the end your folder should look like that: