There have been a lot of deaths on Game of Thrones, but as the series nears its end, it's not surprising that there may be more in store. During the latest episode, Melisandre bid a farewell to Westeros (for now) but told Varys she'd be returning because that is where she's supposed to die. So will Melisandre die on Game of Thrones? It definitely seems likely.
If anyone knew when they were going to die, it makes sense that Melisandre would. Though her belief that Stannis was the Prince That Was Promised was off base, since then she's been pretty good with her Red Priestess skills. She brought Jon Snow back to life and successfully connected him with Daenerys, which almost every fan can agree was a necessity for the world of Westeros.
So it seems fair to assume that Melisandre's prophecy that she's going to die in Westeros is just pure fact. Besides, although some may have forgotten, it was revealed back in Season 6 that Melisandre is actually very old. It's hard to know how old specifically, but I'd wager she's older than Lady Olenna was (R.I.P.). However, it seems doubtful Melisandre will be dying by natural causes.
Instead, it seems more likely that Melisandre's death will have meaning and will have something to do with the Prince That Was Promised. According to legend, the original Prince, Azor Ahai, had to kill his loving wife, Nissa Nissa, with a sword that then became the Lightbringer, which was used to destroy the Great Other.
It's possible Melisandre is the representation of Nissa Nissa and whoever the Prince That Was Promised is will have to kill Melisandre for them to get the powerful sword that will kill the Night King. If that's the case, it seems fair to assume Jon really is the Chosen One. He and Melisandre already have some shared history together. That doesn't exactly equate to a wife, but it's difficult to say how exact these prophecies have to be.
It's possible that she knows it's Jon that must kill her but it wasn't the right time back when they were in Winterfell. It's also worth noting that Jon currently has one of the few remaining Valaryian steel swords left (Longclaw) and it's already been proven that Valaryian steel kills White Walkers. Maybe it's this sword that must kill Melisandre so Jon can then use it to kill the Night King. In short: Longclaw could become Lightbringer — and it could be Melisandre's death that brings it about.
Fans will just have to wait until The Red Woman returns to find out the truth.