From McGill University:

So why do we stop growing, while lobsters don’t? The cells that make up our body are constantly making new cells by dividing. A biological technicality causes us to lose a bit of DNA at the ends of our chromosomes (structures made up of DNA and proteins) after each replication. DNA contains the blueprint for our lives, so in order to make sure we aren’t losing crucial information during these divisions, the long molecules of DNA are protected by shorter segments of DNA at their ends called “telomeres.” An analogy would be the plastic tips on a shoelace that prevent it from unraveling. When a cell multiplies, the only part of the chromosome that is lost is a piece of the telomeres. But as we age, our telomeres get shorter, until they reach a critical point where the cell can no longer replicate without damage to its essential DNA. When this occurs, the cell becomes inactive or dies. Shortening of telomeres is linked to senescence and increased risk of disease. Other contributors to aging include oxidative stress (hence the appeal of antioxidants).

Lobsters have a perpetual supply of telomerase – the enzyme that can restore telomeres, helping cells avoid that fateful end. Humans also have telomerase, just not enough to overcome the constant shortening of telomeres. In fact, telomerase is often found in cancer cells, giving tumours a survival advantage.

Unfortunately for our pal Larry, a large supply of telomerase can be a double-edged sword. Lobsters are still more likely to die with age because their hard-shell exoskeleton moults and has to be regrown. This requires reams of energy, eventually too much. As a result, common causes of death for lobsters are exhaustion, immobility, and shell disease, although the leading cause is still predation.

McGill

The article goes on to say that there are actually some jellyfish that are biologically immortal, meaning they do not age or ever die of old age, although they can be killed.

Given an infinite span of time, the odds of a “biologically immortal” organism being killed would seem to be 100%. So this does not sound like immortality to me in a colloquial sense, But figure out this mystery and come up with a drug to restore our telomeres without causing cancer, and we could live for a long, long time if we are careful. Would our brains hold up more than a century or so?

Interestingly, and this is a frequent point of conversation my son likes to bring up, the Norse gods are “biologically immortal” because they do not age but they can be killed (sorry, Thor fans). But the Greek/Roman gods are truly indestructible. I recall one story where Zeus was cut up into little pieces and put into a bag by another one of the gods. Eventually, somebody let him out and the pieces just assembled themselves together again and he continued being Zeus.