Ferocitus
Deity
I don't know about lobsters, but one would expect (far) simpler organisms to be "immortal", cause they don't have that many organs to regenerate anyway. Maybe something as simple as a type of worm, or a clam like the one in the link
Not that worms are likely to survive in the wild; iirc they are the main food of a vast category of predators.
Re human ageing, apart from biological factors psychology plays a role too. Living for 1000 years would be tougher, i think, even assuming you can not actually age much. Ferocitus' point about being familiar with the state of things in the world is very good; can you even imagine children not suffering from depression if they guess how things are from a very early age?
Those studies of "perfect recall" are like a folie a deux between the researchers and their subjects. (I bet the reports invariably end with a request for more funding!)
I'd also bet that a few questions by an experienced court lawyer would expose the nonsense very soon.
The Ship of Theseus would sail into view within moments.
