Capfka, that is a poignant tale you tell of Lizzy and Demmy. One way to explain Lizzy's behaviour (you might not agree) is, 'Empathy'. She would certainly have known Demmy was ill, you mentioned they were close, and this was probably how she was trying to help. Empathy need not be at cross purposes with survival and propagation. I use empathy, fully aware that it requires a certain consciousness of self; that it takes a certain awareness to be empathetic and I believe most animals have the capacity. We like to limit their behaviour into clearly defined slots, the better for our understanding. Empathy has been studied and documented in chimps and elephants by those that believe.

....another thought...It seems, we associate, (in humans) altruism with money - acts of charity, almsgiving, the like. Rescue operations, like firefighters trying to save people are considered heroic, not altruistic. The same thing in an animal we would not consider heroic, would we?