Lazarus taxon is originally a paleontology term, referring to the disappearance in the fossil record (generally indicating extinction or a very small number of individuals) of a species that emerges again in a much later era. The term is also used in neontology (the study of extant creatures) when referring to a species believed to have gone extinct that is later found to still exist.
In the Book of John, Jesus raises the man named Lazarus, and brings him back to life more than four days after his death. Hence the term “Lazarus taxon” is quite applicable - the species was believed extinct, but was “brought back” in the records as it were, when it was re-discovered after the date of its being declared extinct.
A counterpart to the Lazarus taxa (singular of taxon) is the Elvis taxa. This term is used when a species assumed extinct from the fossil record is incorrectly thought to have re-emerged at a later date, but is found to be a like-looking species that adapted a form similar to the original species, thanks to convergent evolution. The original species did not re-appear, but the impostor species was so similar that the original was believed to have re-appeared when the impostor was first discovered.
This term comes from, well, “Elvis” sightings, and Elvis impersonators. Clearly they’re not Elvis, but some look similar enough at first that they could fool professionals who had no way to confirm that Elvis was dead. The fossil record is so spotty that a disappearance of a species doesn’t always indicate an extinction, and paleontologists are used to many species re-appearing in later eras (it’s less common in neontology), so the first instinct is to classify the discovery as a re-emergence.