Maahey, thanks for at least attempting to come up with some explanation.
Dogs have empathy - it's one of their finest traits and is clearly another outcome of their predisposition to pack living. Empathy under those circumstances seems to be a survival trait in all pack animals. Even hyenas have been shown to have it within the pack environment, otherwise unloveable though they are.
Cats, on the other hand, only exhibit it where they, too, are historically group living and (don't shoot me here!) that would just about be covered off by mentioning lions and cheetahs, although cheetahs are a bit conditional, because they tend to form temporary family groups rather than packs with a wider community.
Cats which are not siblings can "learn" to live together, it's true. We have had cats who got on okay, but the limits tended to be well-defined. Food is one item which has always been outside those limits in my now reasonably extensive experience. Cats will compete for food even where there is plenty for all. What's more, cats who live in a group within a human family are always living in a certain amount of tension. It's rare that cats who weren't brought up together from kittens will choose to sleep together, for instance. There is also no natural approach to social hierarchy among cats, and they will fight - not always physically, of course - to be top cat. Toms don't always win over tabs in this situation, either. Cat group hierarchy is a fluid thing and can change overnight because it's NOT instinctive at any level. Cats usually walk alone, and that difference between them and dogs can pretty much be summed up by Wow's throwaway remark "Dogs have owners; cats have staff".
Cats and dogs can form "alliances" when they live together within a human grouping. I'll never forget our English pointer (Smelly Ella from Portobello) and Red, my siamese red-point tom, chumming up to hunt lizards in the long grass on the next door section. Ella would "point" the lizards. Red would pounce and eat. Since Ella didn't eat lizards and Red didn't need to, I can only guess that it was "play". My chocolate-point siamese queen, Sirikit, would stand on the driveway above the road and yowl at passing dogs - this was sheer bloodymindedness, you understand - but ONLY when Demmy the keeshond was around to object to strange dogs coming into her territory. The cat door was only about ten feet away, too, and Skritters miscalculated from time to time - the cat flap would bang and then there would be a thump as some outraged canine smacked into the door in pursuit! There would be a siamese with an arched back and toilet-brush tail yowling at the world on the inside of the door ...
I guess what this all boils down to is that I would like to agree with your theory about why Lizzy left the rabbit. But I can't!
