I have a Red Devil 5700xt and since updating Overwatch can hardly do anything the game without receiving the rendering device lost error. Back in the older update, I could prevent the error by disabling streaming on Battle. Net for some reason. This no longer works as of the latest patch. I can post a DxDiag but im not sure how to format it correctly.
Greetings Lukerz,
The issues you are facing can easily happen after a game update, specially if your graphic drivers are outdated.
I would start by following this helpful guide that usually solves the Device lost error you are facing:
Should you still have more issues after performing these steps, you can reply back to this post with the system files so we can have a better look at what may be causing this issue.
You can follow this guide that will teach you how to edit the DxDiag and MsInfo files appropriately:
Have a great day!