I think to determine if animals can have such Rights, Rights themselves must be examined.
Using the words or the Declaration of Independence that recognizes and references pre-existing natural Rights, can we say, "We hold these truths to be self-evident, that all lions are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Lions, deriving their just powers from the consent of the governed,--" and have it hold meaning?. When we read that all lions are created equal, this means that all lions are born with the same Rights as all other lions -- neither more nor less.
Issodhos, even though I really hate parsing any of our founding documents, I disagree with your reading here. I'm not good at naming parts of sentences but the commas here, I believe, are used to indicate independent thoughts, as in:
We hold these truths to be self evident -
- that all lions are created equal
- that they are endowed by their Creator with certain unalienable Rights,
- that among these are Life, Liberty and the pursuit of Happiness.
That to secure these rights, Governments are instituted among Lions, deriving their just powers from the consent of the governed,--"
Governments may or may not be instituted among lions, but if they were, their purpose would be to secure these rights - not to grant them.
I would postulate that for individual lions to have Rights, lions as a whole must know that each lion has the Right to life.
Once they figure it out, perhaps they will explain it to the House and Senate.
There are similar problems throughout, but I'll take exception to one in particular:
The fundamental natural Right of Man is self-ownership -- the ownership of one's person.
Clearly the original document did not include women; nor did it include men of color. Only later was that natural Right Recognized.
Were I a lion, I might say that it's simply a natural step to recognize my people. Your arguments on this one are a direct parallel to those used against the non-white and the female. They worked - for awhile - in those situations; as a rhetorical device , I think perhaps their time is over.