Einar isn't really a tough nut to crack. He's born a man, but he identifies as female. He has male sex organs, but he believes he also possesses female organs (and sure enough, he does). In this way, he's a person split in half, being seen as a man while feeling like a woman for much of his life.
The book emphasizes the duality of Einar and Lili with the imagery of things being split in half.
As Lili develops her own personality, with her own thoughts and memories separate from Einar, he sees it like this: "In the skull it was almost as if there were two brains, a walnut halved: his and hers" (5.63). Later, he thinks of himself as "the walnut halved, the oyster shucked open" (9.29). Einar/Lili is clearly a person divided.
Greta gets her own imagery of halves, too, though she doesn't have Einar and Lili's dual personality. One image we get of Greta is particularly intense:
Had she really been the type of child who would cut [frogs] in two with a butter knife thieved from her mother's pantry and then present them to Carlisle on a plate, beneath a silver warming bell? (28.7)
What kind of kid does that? Scary childhood antics aside, this is interesting because Greta is the one who sort of splits Einar in two since she puts the dress on him, and she names him Lili. And Einar and Lili's chance for survival is about the same as the poor frog.
In the end, Greta is on a ship whose prow splits the water "into halves, cutting what had once seemed interminably one into two" (28.40). We have a feeling Greta will now think of her own life in two halves: before Lili and after.