For an interesting analysis, consider the title as a double entendre, having two meanings. On the one hand it seems obvious that the plot is related to The Lives of Animals, because Elizabeth Costello is a lecturer on exactly that topic, explaining her philosophies about how animals experience reality and suffering, and that human processes that neglect this are wrong. On the other hand, Elizabeth herself is an animal too, so this also about her life as an animal.
By viewing Elizabeth as part of the animal kingdom, the book comes into focus. Her lecture about Nazis is questioned by others in the book, but to Elizabeth it is self explanatory. The Holocaust (in her opinion) was about dehumanization. But Elizabeth is extending that dehumanization to animals which are literally not humans, but still suffer, according to her lectures.
To suggest that animals can be dehumanized is to also suggest that animals are valuable in the same ineffable way that human beings are. In other words, she is extending empathy to all of nature, not just to the animals. This is a good reason to view the title as referring to the humans and animals both, because Elizabeth's own opinion is that the two are essentially similar, or perhaps even the same. She views animal suffering as suffering, and wants to reduce cruelty in the universe, whether cruelty against mankind or the animal kingdom to which mankind belongs.
