Klingon and Human seem to top out at about 100 years and the Vulcans make it to about 200. Is there a UFP member species who last longer?
For a species that is definitely part of the Federation and is TV-Canon, I submit to you The Trill.
Though this depends on what you mean by 'longest lived'. Individual hosts certainly seem to have a limit on their lifespan, and non-joined Trill presumably also die within the same span, but judging by how frequently their symbiote can join, their effective lifetime of a joined Trill could be considered 'infinite' (there is no solid canonical lifespan established for the symbiote, but they seem to live at least as long as 500 years or more under ideal host conditions).
The Horta, who join the Federation after the events of The Devil in the Dark can live for up to 50,000 years. They are only listed as Federation members in novels, but from their only onscreen appearance it is a fair assumption they joined. I know of no other Federation species that can live that long, though certain species like the Douwd, which live in the Federation in secret, can live longer.