By that token normal reproduction qualifies as immortality as parents share a lot more DNA with their kids than those cell lines with their originator. Biologically those cell lines are generations of new organisms not the same individual living indefinitely.

Further those cells can’t compete out in a forest somewhere. Going multicellular means optimizing in ways counterproductive to survival on their own. But failing to cull off defective cells means you can’t have a functioning multicellular life form, thus making this a dead end.

So no in nature there isn’t some switch that means those cells get to survive indefinitely. The closest viable option is as an infection shared among very closely related organisms, but that’s not a stable option which means it’s really rare in nature.

> By that token normal reproduction qualifies as immortality ...

As a kind of immortality, yes. It's not even just DNA, it's actual cells that were part of the individual that stay alive beyond any age limit.

Does it keep the full individual organism alive? No.

My point is because it doesn’t qualify at the organism or cellular level this doesn’t either.

> actual cells that were part of the individual that stay alive beyond any age limit

Neither the egg or sperm or egg cell survive to birth. Only descendent cells with wildly different DNA do.

I think given that all your cells directly are the egg, there is a strong argument to be made of the reverse.

Close to 100.000 cells make the reverse change, in girls (they become egg cells, and potentially the next generation). There's a continuous cycle keeping (some of) these cells alive. A cycle that has been running one way or another, for 4.3 billion years.

Biologically when a cell in invaded by foreign organism who inserts it’s DNA and the cell now spits out copies of the foreign genome that’s often a viral infection. From that perspective it’s arguably the sperm that’s preserved and using the eggs cellular machinery. In either case calling it the same organism is stretching the definition of same well past its breaking point.

Like you can apply the word “same” if you want, but what’s actually happening is isn’t a simple continuation of the original organism any more than a clone is the same organism and at least that’s more closely related genetically.