I think that question is key to understanding what rights are and how they function in the constitution of a polity.
Animals, rivers, etc. don't interact with us in the way other humans do. There may be analogous aspects to that interaction, so we can recognize that we have a responsibility to keep rivers clean, but that's an obligation on our part, not a "right" that the river has.
No, because other animals don't have mental capacity to truly understand the consequences of their action.
That said, I've never really seen a consistent argument against _protecting_ prey animals from lions (and letting lions die out).
You might begin your research into this subject with reading about the reintroduction of wolves into various locations where they had been eliminated. The prey populations always fare better when there are predators around them. Without the pressure of predators to balance the population, deer and beaver and other prey animals tend to over-populate, which results in damage to the environment (over-grazing) and then eventually starvation of the prey animals.
The deer are either going to be killed by a wolf, killed by a human, or killed by disease and starvation. At least the first two options don't also cause extensive damage to the environment before they happen.
https://www.yellowstonepark.com/things-to-do/wolf-reintroduc...
I'm not convinced that dying of starvation is better than a sudden death. The vehicle accidents harm humans as well as the deer. The hungry deer damage crops and gardens.
I think the overpopulation also causes the spread of parasites (ticks etc.) which carry disease.
A lion knows full well that it survives another month when it kills a wildebeest and that it can feed it cubs. What more is there to "truly" understand?
A lion is not, to the best of our understanding, capable of understanding that killing another animal will cause grief to that other animal's family. If that other animal's family is even capable of understanding and/or grieving their death. And then we'd have to prove the killing was done with malicious intent, because just merely being responsible for someone's death, even as a human, is not immediately a criminal offense.
But it's a silly argument anyway because humans are often not prosecuted for the death of non-human animals, especially when that non-human animal is killed for food. So the idea that we would prosecute a lion for killing and eating an antelope is laughable when we don't prosecute a farmer for killing a cow for food.
Alternatively, prey animals would have to have the right to birth control, whereas predators would require a food program. Both would need to be provided by humans, of course, which would inevitably lead to an animal welfare state.
And your example of prosecuting a lion is unfortunately already reality https://en.wikipedia.org/wiki/Mary_(elephant)
Saying a being is a "natural resource" is just despicable. Someone else could say that with equal ease about your family. Would you like that?
Animals are fundamentally incapable of grasping the concepts of rights and would not respect them. Applying human standards to them is fundamentally anthropomorphic chauvinism and absurd hubris.
Under human standards we should start hunting or capturing more male lions because they would happily commit infanticide to make lionesses reproductively available. Naked mole rats are incestuous pedophiles. It is important to remember that nature does not care about you and cannot care about you.
Second, as I have shown earlier humans already do "prosecute" animals for such behaviour. So why would argue that "absurd hubris" should be applied in these cases?
Third, my point was not to start "prosecuting" other animals, but that humans do not follow their own standards.
Mockery or not, it happened and still happens. Only two years ago in Cincinnati. That was technically not "punishment" but the result was the same.
My main point is not whether or to prosecute other animals, but that humans live double standards.
If rivers have rights does it also has responsibility and culpability? What happens if a river overflows and few people drown? Do we punish the river?
A question in the title aside, I love the advocacy embedded in the title. "A growing movement"? From what to what? 2 to 3 people? The article is trying to grow the movement, it isn't reporting on a growing movement.
The only way to give rivers rights is to give it personhood rights in the same vein as corporations. But that means that rivers become privately owned entities. Do we want rivers to be owned by shareholders?
Rivers, like animals, are natural resources. Nations and states are stewards of it.