The Lost Hero picks up six months after Percy Jackson & the Last Olympian ended. New cabins have been built, Percy is missing, and three new demigods arrive at Camp-Half Blood to begin a quest that will lead to a war that could destroy heroes and gods alike.
Piper is a Cherokee girl who gets into all sorts of trouble just to get her father's attention. He's an A-list movie star, so she doesn't have much luck except when he sends her off to reform schools.
Leo is a Mexican-American guy who has a way with machines. Orphaned at a young age, he keeps the pain of his past in check through humor and creativity.
Jason is their friend, or so they think. The cute blonde guy Piper thinks is her boyfriend, and Leo thinks is his best friend, just happens to show up on a field trip, but the Mist convinces them they've known him for months. On top of that, Jason doesn't remember anything about himself or where he is from.
The Lost Hero shares a lot of things with the first Percy Jackson series--young people must go on a quest across North America where they will learn their strengths and weaknesses, a great evil threatens to rise, and the gods are still immature and in need of their kids to rescue them. But it is different in important ways, too. The Lost Hero is darker in tone. Characters are older and angrier; they have more at stake and might be willing to betray friends to achieve their save their loved ones. The humor is still there, but there aren't as many gut-busting moments as there were in the first series. Riordan's stronger writing skills make up for it. But an editor should have insisted he not end almost every chapter with "Then (something dramatic happened)."
Neither Leo nor Piper are white, and Riordan actually gives them cultural identities rather than just saying they have brown skin, but making them act like white kids. They are the two most compelling of the three (Jason's story takes some time to get into. Giving the guy amnesia for most of the novel took a toll on his charisma); their stories are frightening and epic, and reading about them overcoming their personal tragedies truly feels like seeing heroism.