OK, now I have to ask - what are the odds of a sapient carbon lifeform attaining immortality?
How do you define immortality?
Theoretical Immortality - eg; you don't age, you don't get cancer but if you get hit by a car, get some cytokine storm illness, and similar threats it will still kill you. Ergo, eventually, one of these threats will get you.
True Immortality - Nothing can kill you.
The latter is impossible as I see it - we'd have to get rid of these meat bodies first.
The former is likely possible, especially if there are periodic interventions from outside sources (also known as medical care). I don't see anagathics as being a pill or anything like that. What's more likely to happen is that a species (humans?) reaches some tipping point in the understanding of biology where conditions are being cured faster than they kill people. There's proof that the Ancient Egyptians knew about cancer. However, it wasn't the huge life-ending terror it is now, not because we're getting cancer more often now but because were other things that were killing us sooner and more often. Now that many of these threats that killed us in the past are being managed much better, people are living long enough to be struck down by cancer as opposed to other causes. Even as the current crop of human killers are being cured, new ones and more likely old ones that weren't a big problem before will become the primary killers now that they have no competition will become the new killers. Eventually, they'll be cured, only for another set to crop up. This will go on for a while, but eventually our knowledge of biology will get to the point where we're finding solutions faster than people are dying to those problems, at which point we'll have achieved theoretical immortality and the last killers will be things like physical violence or diseases that get us too quickly to be managed.
I bet there are protozoans and amoebas that may have survived for more than a millennia.
Single-celled lifeforms that reproduce by binary fission (dividing) are by definition immortal. When an amoeba divides, which one is the "original"? Unless you define these lifeforms as "dying" when they divide (to be replaced by two identical offspring), they're immortal. Some of these lifeforms do have "spore" forms which aren't really the "same" being so a population in an area might die, but apparently there are lifeforms that don't spore so they'd be immortal by definition.