The Lost Hero has so much plot, Hercules couldn't lift it, Hermes couldn't run around it, Argus—with all his eyes—would need to ask some Cyclopes to help him to see to the end of it, and Olympus itself would look up and say aaargh before being swamped in great snow-drifts of plot, until Zeus had to put on his boots and overcoat and go out with a shovel to clear the golden sidewalks.
Okay, maybe we're exaggerating slightly. But still. There is a lot of plot. We're just going to hit the highlights here, so don't be fooled into thinking this is all that happens.
Jason wakes up on a school bus and realizes he has amnesia. He's with a girl named Piper McClean, who says she's his girlfriend, and a boy named Leo Valdez, who says he's his best friend. They're all on a field trip to the Grand Canyon as members of a school for troubled kids. Once they get to the canyon, they're attacked by storm spirits (which is not something promised in the tourist brochures). Their counselor, Coach Gleeson Hedge, reveals that he's a pugnacious satyr with hooves and horns, and fights to protect them. Jason, much to his own surprise, pulls out a coin that turns into a magical sword and beats up storm spirits, driving them off. As the storm spirits leave, they take Hedge with them.
A chariot arrives piloted by Annabeth Chase. She's looking for her boyfriend, Percy Jackson, who has disappeared. (Percy is famous for his own series of books. If only Jason had read them, much confusion could have been avoided…) Annabeth is disappointed that Percy isn't there, but takes Leo, Jason, and Piper back to Camp Half-Blood, where they all find out they are demigods. Leo is a son of Hephaestus , Piper is a daughter of Aphrodite, and Jason is a son of Zeus or Jupiter, though he's been chosen as the champion of Zeus's wife Hera.
Also, everybody discovers they have superpowers. Piper can charmspeak people and make them do what she wants, while Leo can control flame. You'd think this would make them happy, but it doesn't. Piper has been having dreams of an evil giant who has captured her father, and she's afraid she'll have to betray her friends or the giant will eat her dad, while Leo is afraid to use his fire powers because he thinks they resulted in the death of his mother. Jason doesn't remember his family, which in comparison seems like maybe it's for the best—though he does figure out that Thalia, one of the Hunters of Artemis (out of camp at the moment), is his sister.
Through various prophecies and surprise revelations and then more prophecies, the heroes discover that they need to go on a quest to rescue Hera, who is being held captive. Leo fixes a malfunctioning magical robot dragon named Festus to give them transportation, and up, up, and away they go, dragonning across the continent to Quebec, Chicago, Detroit—just all over the place. On their way they meet and/or battle lots of evil gods and mortals and critters, including some Cyclopes, Medea, King Midas, wolves, and who knows what else. They rescue Coach Hedge, the battling satyr, along the way. Also, Festus the dragon gets wrecked, which is sad.
As they bump along they get even more prophecies and dreams and clues, and eventually put it all together to figure out that the earth mother, Gaea, is awakening, which is bad. Gaea has captured Hera, and plans to destroy her and use the energy to summon the giant Porphyrion, which will be even worse. They also meet Thalia (this, thankfully, is a good thing)—Jason's sister—who tells them that Jason was given to Hera when he was two, at which point Thalia thought he was dead. Meanwhile, Piper decides that she can't betray her friends, and tells everyone that her father is in trouble. So Leo, Jason, and Piper send Thalia to try to delay Gaea and Porphyrion while they go off to rescue Piper's dad from the giant Enceladus.
There is a big amazing super-battle with Enceladus, who loses like the bad guy that he is, because that's what bad guys do. Piper saves her dad, Trevor McClean, and gives him a magical potion that makes him forget about the kidnapping and gods and all that because it was freaking him out, and no wonder. Coach Hedge takes Trevor under protection. Leo, Jason, and Piper scurry off to help Thalia try to prevent Gaea from waking.
There is another even bigger, even more amazing super-battle with wolves and air spirits and so on. The bad guys lose because they are losers, etc. Hera is freed, Gaea doesn't wake up, but Porphyrion gets away to fight another day. Curse you, Porphyrion.
Once they get back to Camp Half-Blood, Leo starts to build a giant flying ship to take them on their adventures, using pieces from the broken Festus, while Piper and Jason move toward being boyfriend and girlfriend. Ooh, aah, and ooh la la.
Most importantly our heroes figure out that Jason comes from a whole other group of demigods who are children of the Roman, rather than the Greek, aspects of the gods. The Roman and Greek demigods were separated by the gods because they kept killing each other. But now Hera is trying to reunite them so that the seven demigods foretold by prophecy can kick Gaea's earthy butt. Hera brought Jason to the Greek Camp Half-Blood to be a bridge to the Roman camp. Similarly, they realize Hera sent Percy Jackson over to the Roman camp, where he probably has amnesia. We have now run out of plot though, and won't know for sure about Percy until the sequel (titled The Son of Neptune).