In “Requiem for Methuselah” Kirk and Spock encounter a human man calling himself Flint, whom they learn was more than 6,000 years old, and over the course of history was also Soloman, Alexander the Great, Lazarus, Merlin, Leonardo da Vinci, and Johann Brahms.
Then, in “The Broken Circle”, Pelia becomes chief engineer of the Enterprise and we’re told she’s a Lanthanite, and extremely long lived species who resided on Earth, living among humans. She claimed to be at least 5,000 years old herself in “The Sehlat Who Ate Its Tail”.
I think it’s a reasonable possibility that Flint was a Lanthanite himself, or perhaps part Lanthanite, without being aware of the fact. That would account for his long lifespan.
Granted, we don’t actually know how long Lanthanites have been living on Earth. At least since the 1980s, but that’s as far back as Pelia has mentioned. Also, if Flint’s stories are accurate he is highly resistant to physical damage, having recovered from being stabbed in the heart. Pelia isn’t affected by LSD or Chapel’s epigenetic serums, but we’ve never seen her be physically attacked. Also, in “Requiem for Methuselah” Spock makes no mention of Lanthanites. Obviously from a real world perspective, it’s because they didn’t exist until season two of SNW, but in universe he is certainly aware of their existence, so we might extrapolate that, for whatever reason, he doesn’t believe Flint is a Lanthanite.
It’s an appealing theory, but how would you square it with the end episode reveal that Flint was no longer immortal since having left earth? Was McCoy just wrong when he reported that readings from the earlier tricorder scan show that Flint has been aging normally since he left Earth’s environment, and will soon die? We know little enough about Lanthanites in general, and Pelia in particular but it is implied that they are an alien race, so their long lifespan isn’t likely to be linked to remaining on earth, unlike Flint’s. Perhaps it wasn’t leaving earth that cancelled Flint’s immortality, but some element on Holberg 917-G?