"Aren't you a pretty man," she had said, years ago, when they were first alone. (1.27)
Einar always has a feminine appearance, which likely assists him in his transition. It is very easy for him to pass as female even before he has any sort of surgery.
Einar Wegener/Lili Elbe
"But I can't wear Anna's shoes," Einar said. (1.11)
Einar initially resists dressing like a woman because he would be embarrassed for his wife, or anyone really, to see him in feminine clothes. But he soon comes to embrace it. You do you.
One day Greta plucked her eyebrows and they never grew back, which she saw as more of a convenience than anything else. (2.3)
This is a small line, but it illustrates that Greta is a woman accustomed to having an unusual appearance. Therefore, she won't find her husband's appearance unusual when he begins to dress more femininely.
Lili left Hans on the steps of the police station, turning three corners immediately, running away from him […] the stain on her dress spreading as persistently, as appallingly, as a disease. (9.95)
Lili's bleeding is a medical problem, but the stains it leaves are an external parallel of her internal feelings. She is hurting inside, agonizingly torn between two possibilities.
"What would you think if I were to tell you to stop dressing as her?" (11.40)
One of the doctors Einar sees thinks that a man in woman's clothes—even if that man identifies as a woman and everyone else thinks of him as a woman when he's in those clothes—would be damaging to the fabric of society. That doctor is a bit of a quack.
Part 2, Chapter 13
And so Einar would set out from the ladies' pool in Lili's clothes, with the rubber bathing cap still on his head. (13.19)
In Paris, Einar dresses like Lili even when he doesn't feel like Lili. It's interesting that Einar can appear as Lili even when he's Einar—he and Lili have a complex dual identity.
Einar was a man with suspicious stains on his clothes. (13.25)
Early on, Einar is happy with his own identity. Well, if not happy, he's at least satisfied. But he begins to get more and more concerned with how he looks to other people, and he wants to look like a woman to them so he can feel more like a woman himself.
"He came to see me, and the first thing I noticed—how could I not?—was that he had breasts bigger than many teenage girls. […] I discovered he was both male and female." (16.37)
It is lucky that Greta is able to find a doctor who once met a man similar to Einar—a man who looked female and wanted to continue on a surgical path to look more like a woman.
Einar Wegener/Lili Elbe
"Do I look like Lili?" Einar said. "Do I look like a woman to you?" (17.73)
Einar is being defensive here, but deep inside, he desperately wants the answer to be yes. He wants to look like a woman all the time now, and in order to do that, he needs to shed his Einar suit.
"Professor Bolk thinks he can change Einar into a woman," Greta said. "Not mentally, but physically." (18.30)
Mentally, Einar has been a woman for a while, but at the end of the book, it's the physical part he needs help with. He wants to look like a woman in clothes and out of them.