In the first book, the character Genarro actually lives, and isn't ignominiously eaten while on the toilet like he was in the movie. He even gets to beat up a raptor. By the second book, he's died of dysentery.
Accidental inversion in that Ian Malcolm, the main character of the second book, dies at the end of the first one. He gets better, though.
The main character of Raymond E Feist's Mistress of the Empire series spends the first two books in various political machinations to secure her title and lands. The triumph of her goal is to have a son, who dies in a faked accident two pages into the third book.
In the third book of The Elric Saga by Michael Moorcock, Count Smiorgan Baldhead, who had traveled with Elric in the last book, gets unceremoniously abandoned by Elric and left to his death during the battle with Melnibone. However, Elric does get called out on it. It also turns out that this is actually an inversion, since Smiorgan's death occurred in the very first Elric story ever published. However, that story was relatively far into Elric's continuity, so he got brought back later for another story set earlier. Later collections published the stories in their order in continuity, rather than the order they were originally published.
Empress Nerissa and her entire family die offscreen in a bloody assassination just before the opening scenes of the second book of Patricia Bray's Chronicles of Josan trilogy. Considering her importance in the first book, this comes as a bit of an immediate shock, but it isn't done wastefully or for no reason. Her death shapes the circumstances surrounding Josan's life for the entire rest of the trilogy.
Then in The Last Battle, Eustace and Jill learn that their friend from the last book, Rilian, "has been dead for over two hundred years." Presumably Puddleglum has, too. In fact, that book begins with the deaths of everyone from our world who ever visited Narnia, exceptSusan, in a train crash. But due to Narnia doubling as some kind of entrance to the afterlife, nobody actually notices they're dead until the end.
Shadow Moon, a sequel to the movie Willow, kills off Madmartigan and Sorsha in the first chapter.
Between books 11 and 12 of Ranger's Apprentice, Alyss and Crowley have both died, and King Duncan is on his deathbed. Also, Halt is retired.
Uncle Press, the uncle of Bobby Pendragon, is killed off in the second book of the literature/Pendragon Adventures series, so that Bobby can take his role as head Traveler in the fight against Saint Dane.