We know that Ella has read the Sibylline Books - the books of prophecy that outlined the entire history of Rome, said to have burned when Rome fell.
"Never mind," Frank said. "Listen, we've got to protect Ella, take her with us."
"Of course," Hazel said. "The poor thing needs our help."
"No," Frank said. "I mean yes, but it's not just that. She recited a prophecy downstairs. I think... I think it was about this quest."
"The thing is," Frank said, "Ella remembers everything she reads. She said something about the page being burned, like she'd read a damaged book of prophecies."
Hazel's eyes widened. "Burned books of prophecy? You don't think - but that's impossible!"
"The books Octavian wanted, back at camp?" Percy guessed.
Hazel whistled under her breath. "The lost Sibylline books that outlined the entire destiny of Rome. If Ella actually read a copy somehow, and memorized it -"
The Heroes of Olympus, book 2:
The Son of Neptune, chapter 36
We also know that demigods have more powerful dreams than mortals - they can see things in places where they aren't while in a dream, communicate with other people... it's even revealed in The House of Hades that it's possible to die in a dream.
All this, plus the fact that Rachel Elizabeth Dare recited the Prophecy of Seven at the end of The Last Olympian (which means that it fits with previous example to have a prophecy about the next series at the end of one series), makes me assume that yes, this is a hint for The Trials of Apollo.
And of course, these lines make an appearance in The Hidden Oracle.
The voice spoke again: FIND ME.
This time it was so loud, it stabbed through my forehead like a railroad spike. I stumbled, falling to my knees.
"Hey!" Meg gripped my arm. "Get up!"
"You didn't hear that?"
THE FALL OF THE SUN, the voice boomed. THE FINAL VERSE.
I collapsed face-first into the stream.
The Trials of Apollo, book 1:
The Hidden Oracle, chapter 9
I'd say that this is fairly conclusive that yes, this is relevant in The Trials of Apollo.