I think the lions and tiger contracted the virus back from people because those two species are/ were found in China and those particular species will be susceptible to it. Just like any other species from China or Eurasia might be able to get it.
The original virus could have come from predatory animals in which case it will probably be confined to big cats and other meat eaters, including people. It might have come from vegetarian animals but I doubt that.
I doubt cattle will get it but they might, and if they do, we're screwed. However, if you cook meat properly, it will kill any viruses in or on it. So no rare or medium rare meat, always well done.