When will I be able again updating via liveupdate without having problems after?
I cannot possibly tell, because if the issue was your local cloudflare not not updated yet, it's not something I can test of verify. And if it wasn't updated yesterday, it might be in the next days, it's something that is completely out of our control.
The best way to know, it's just try and, if it doesn't work (you still get the error), just run the Offline installer again.