and peace to you... is why would you want a PET lion? Why couldn't the lions... and tigers... and whatever other animals there are just, well... BE? Like the people: FREE?
Since there won't be "domestic" AND "wild" beasts... but just beasts... why should we want to have any as our "property"? Because that is what a "pet" is: the property of the human that cares for it. Usually for companionship or entertainment. Such thinking, however, is truly human... and fleshly. What if the tables were to be turned, that they would have the privilege of possessing us? Were that the case, I would wager that they would endeavor to take better care of us than we have of them.
In the kingdom of God... NO living thing, regardless of its KIND... is POSSESSED by another, dear one. And none will need the care of another... regardless of its kind. Right now, animals... both domestic and wild... are in subjection to man. That is NOT because man is superior, however, but because we are DIFFERENT: we have physical capabilities that they don't have. In particular, the capability of oral speech. Because they don't possess such capability and are, therefore, dumb (mute), "we" very often view them as "dumb" as well. That, however, is not entirely the case, as any pet owner will tell you. True, a dog may not develop much past the mental capabilities of a toddler, but most toddlers aren't as smart as most dogs.
My advice? Enjoy your dear pets now... but perhaps you can start thinking of them as fellow fleshly BEINGS... living, breathing and, in many cases, THINKING beings, albeit of a different KIND, that DO need our care now... but SPIRIT beings what WON'T need our care... and won't exist for our personal companionship, entertainment, work... or food... then.
Oh, and to answer your question, no: there will be no death. For "man" OR beast.
I bid you peace!
A slave of Christ,