THESE SHALLOW GRAVES
Nobody ever found out that it was Alpheus who'd killed Lilith, that it was Alpheus who had helped the good guys prevail. Perseus hadn't stepped foot off of the battlefield, had never went to go meet the demigods in the cavern. He'd been dead by then. Perhaps the demon had had a change of heart after he'd killed his brother, and perhaps that was the reason why he'd shifted into a form that was about the age of Perseus, masquerading as his identical twin, which would explain why he didn't fight Lilith in his true form; they would've seen the difference in fur length. Alpheus' true name is, indeed, Belial, since Lilith's incredible sense of smell made it capable of her to discern the difference between the twins. Of course, it would be easy enough to say that Alpheus disappeared off the face of the Earth, that he never showed his face again, but in doing so it would be terribly wrong
Jason and Piper occasionally see a disembodied shadow flit in and out of their apartment on certain days, doing nothing more than looking and then leaving, as if it were checking up on them. They always assumed that it was Nico. Something went terribly wrong during the War Games, something that the medical eagles couldn't get to in time; a young probatio had toppled off the side of the fort, plunging to what was almost certainly her death, but when everyone ran over to what they supposed was her crumpled body, they found her unconscious but still alive and breathing, and many claimed they saw a super-fast specter swoop out from the shadows and catch her in midair, disappearing as soon as it had come. Again, many assumed that it had been Nico, and the son of Hades was more than confused when people hugged him tightly and thanked him for saving the girl's life.
Speaking of Nico, he and Will moved to the cities, and their neighbor just so happened to be a kind, warm-hearted woman by the name of Sally Jackson. She was childless, having divorced her pig-headed husband Gabe a long time ago, and she kept lamenting to them about how wonderful it would be to have children, though she still had yet to adopt or artificially inseminate, and she was hesitant to do both. In return for babysitting their daughter (and saving her from a rabid hydra without knowing it), they left at her door a cradle embellished with shells. Inside was a son of Poseidon whose mother had died giving birth to him, and the god had taken his son to Camp Half-Blood to be raised. Not for nothing, but the campers were shit parents, still young and training, and Sally seemed like the perfect mom. The mortal had rushed over to them at once, boasting a swaddled little baby and beaming. She asked them what she should name him, fretting over the fact that she hadn't had time to think of a name, and they took one look at his startling green eyes and replied, "Perseus."
Though the murder rate for mortals had inclined drastically over the last few years, the demon population had suddenly plummeted drastically, and small miracles were beginning to happen. A little girl watched in a mix of delight and horror as a lightning fast shadow plucked her dog from oncoming traffic and placed it in her arms before disappearing. A woman screeched to a halt when she saw a green-eyed boy standing in the street, only to get out of her car and find the boy missing and a deer leaping across the street, one that she would've hit (and the impact may have killed her) had she not stopped earlier. The Reticulated python outbreak in the Everglades was suddenly nonexistent after a visit from a Kindergarten field trip, one that held a boy that nobody knew the name to and thoroughly avoided.
Leo and Calypso were nearly killed when Festus malfunctioned and went spiraling to the ground from a mile into the sky, only to find the dragon halt about four feet from the ground and then collapse, as if he'd been placed down gently.
Annabeth received an apology letter from an anonymous person, who felt guilty for supposedly killing a suitor, yet nobody was missing from the camp, though people did point fingers at Harley since they'd seen a particularly small person slipping into the Athena cabin that night, though the Hephaestus had adamantly denied it.
Sally's Perseus grew up to be almost as much of a hero as Nico and Will, and it was startling just how much like the real Perseus was, and they nearly summoned him to accuse him of impersonating a baby, though the demon was still off the radar.
Maybe Perseus achieved Elysium and decided to rebirth, and perhaps Alpheus knew that, considering the son of Poseidon never seemed to be challenged by monsters; in fact, no monsters were ever detected within a mile radius of the demigod, but that's only a theory; it's up to you whether you want to believe it or not.