So basically what Christians believe is that after God banished Adam and Eve from Eden, the whole world changed due to sin. God said everything he created was "Good", which means that there was no death yet at that time. So when the original sin happened, everyone and thing was banished and basically animals started to rely on other animals to survive. And that's why there's that verse where it says the lion will soon lay with the lamb, or something like that. So basically we believe that all animals and humans await for the second coming.
But thats one interpretation. I'm more leaning toward the evolution viewpoint where the 7 days of creation are actually just describing the events of the history of the universe. Theres a theory that says that in acient hebrew, there wasn't a word precise enough to describe days, and the closest interpretation was actually "a period of time". So 7 periods of time described the creation of the universe as we know it, humans being the last thing to have evolved persay until the bible's story starts. And we believe that the death of animals isn't actually "bad" because death for animals was a normal thing, but for a creation made in God's image, death was definitely not a good thing.