They live until they die, usually by violence, which by Winter standards is listed as “Natural Causes”
A few Fae are genuinely immortal, the Queens, Kringle, The Erl King, most likely Lea. Physical or magical attack can’t kill them, only dissipate them for a time. I would add to this list Puck the Wildfae who is shown to be at Leas power level, and likely Eldest Gruff from Summer, who seems to be Titania’s second and probably more powerful than Sarissa.
I think that is a matter of power with the Lady’s just powerful enough to be Immortal. Nameless is probably under the Lady’s power level (which supports the Cowl theory, the Word would have made him immortal(here’s a thought Cowl achieves immortality on Harry’s birthday, only to be immediately killed by Harry)) and able to break free from Mab.