Who says the lion is just needlessly cruel? Fundamentally neither of us can know what's happening in the lions head so there is no empirical evidence to be had. With passing judgement I tend to work on innocent until proven guilty so I'm just gonna assume the lion is acting on instinct.
As for your main argument of "all animals have a right to kill other animals in order to defend or feed themselves" if you combine that with your other argument of humans and animals are equal, can a human kill another human for food? Can a human kill another human in defense of a slap? This right your proposing is missing a key part and that's necessity. If it is necessary, or the animal thinks it's necessary for its survival, then that animal has a right to kill for food or defense. This is where modern humans and animals are different, humans are far more aware of what is and isn't necessary for survival. A chimp doesn't know whether it will or even can get enough food from just plants. Your average human, at least in the developed world, is aware that you can survive off a vegetarian diet and there is food available to do so. They wantonly choose to kill animals because they taste good. I also don't judge people close to subsistence eating meat because they need every calorie they can get.