Why Does James Come Out of Voldemort’s Wand Before Lily?

He doesn’t.

In most editions of the book, that is. In the original, first edition printings of Harry Potter and the Goblet of Fire, there is a mistake. That night in Godric’s Hollow, James died first, and then Lily died protecting Harry from Voldemort. If the ghosts come out of the wand in Priori Incantatem in revese order, then Lily should come out before James. But, the order of the last two ghosts who emerged from Voldemort’s wand was originally reversed:

And now another head was emerging from the tip of Voldemort’s wand … and Harry knew when he saw it who it would be … he knew, as though he had expected it from the moment when Cedric appeared from the wand … knew, because the man appearing was the one he’d thought of more than any tonight …

The smoky shadow of a tall man with untidy hair fell to the ground as Bertha had done, straightened up, and looked at him … and Harry, his arms shaking madly now, looked back into the ghostly face of his father.

“Your mother’s coming …” he said quietly. “She wants to see you … it will be all right … hold on …

And she came … first her head, then her body … a young woman with long hair, the smoky, shadowy form of Lily Potter blossomed at the end of Voldemort’s wand, fell to the ground, and straightened like her husband. She walked close to Harry, looking down at him, and she spoke in the same distant, echoing voice as the others, but quietly, so that Voldemort, his face now livid with fear as his victims prowled around him, could not hear …

GoF First Editions pg 667/579

According to her official website, J.K. Rowling had originally written that Lily emerged from the wand first. However, her American editor, in the rush to edit the book, incorrectly pointed this out as an error, and Jo “changed it without thinking.” Subsequent editions of the book corrected the mistake, and the text appears correctly, like this:

And now another head was emerging from the tip of Voldemort’s wand … and Harry knew when he saw it who it would be … he knew, as though he had expected it from the moment when Cedric appeared from the wand … knew, because the woman was the one he’d thought of more than any tonight …

The smoky shadow of a tall woman with long hair fell to the ground as Bertha had done, straightened up, and looked at him … and Harry, his arms shaking madly now, looked back into the ghostly face of his mother.

“Your father’s coming …” she said quietly. “Hold on for your father … it will be all right … hold on …

And he came … first his head, then his body … tall and untidy-haired like Harry, the smoky, shadowy form of James Potter blossomed at the end of Voldemort’s wand, fell to the ground, and straightened like his wife. He walked close to Harry, looking down at him, and he spoke in the same distant, echoing voice as the others, but quietly, so that Voldemort, his face now livid with fear as his victims prowled around him, could not hear …

GoF pg 667/579

It’s not known if this “error” will make first editions of this book more valuable than other first editions in the future, but if you own one of these incorrect versions of the book, you own something special!