This brother and sister duo, Cal's grandparents, are like the Wonder Twins, but with fewer superpowers and a little more incest. Maybe. We have no idea what those Wonder Twins are up to when they take the form of a mop and a bucket.
Desdemona is always a nervous wreck. She focuses on matchmaking for others, fretting about the people she loves getting married, and nurtures a little bit of hypochondria for herself as well. She's also quite the drama queen, like her half-page rant about the dangers of gambling that ends with her calmly declaring, "in a practical tone, 'Now we have to move in with Milton'" (2.7.55). But isn't this all what you expect of a Greek matriarch?
As a young man, Lefty is kind of the opposite of his sister. Instead of retreating into himself like Desdemona, Lefty is extroverted. He's a bar-hopper and a womanizer, but—and here's the kicker—it's only because he's trying to avoid his taboo love for his sister. "Sometimes you don't even notice what's right under your nose" (1.2.73), he says.
The destruction of Smyrna is a blessing in disguise for Lefty and Desdemona. Were it not for that, they never would have left their small Greek village. However, on the boat to America, they're allowed to pretend to be other people and eventually marry each other. When you ignore the fact that they're brother and sister, it's kind of sweet.
In Detroit, Lefty and Desdemona move in with their cousin Lina and crank out two kids. They're living the American dream (i.e. whitewashing their culture in order to live exactly like everyone else) but they're victims of a gender-segregated society. Lefty works while Desdemona stays at home, and Lina's husband, Jimmy Zizmo, believes that women belong in the kitchen and men should be socializing and smoking cigars. This belief system drives the men and woman apart and makes them unhappy. Plus that cigar smoke is never coming out the slipcovers.
Desdemona seems to enjoy adhering to gender norms, or at least, she does it and finds a way to cope with the fact that she's doing it. "Having grown up in a country ruled by others, she found it all familiar" (2.4.1). Plus, girl can cook and takes her time in the kitchen pretty seriously.
Things change when Desdemona has to leave the house and get a job. Working for the Nation of Islam is a pretty big deal, mainly because their fezzes remind her of the Turks who destroyed her village and so her interaction with them is a way of reconciling her past. However, she goes a little too far into the "I hate everyone" realm of rationalization when she decides that all white people are evil. (Stuff white people like: genocide, slavery, sweater vests.) Because of this fear, she has her tubes tied and never has kids again.
Meanwhile, Lefty ends up losing his job at the Ford factory simply for living with Jimmy Zizmo, whom various head honchos don't think is American enough. This leads Lefty to working with Jimmy to smuggle liquor into Canada. Who knew Canada could be so scandalous?
People get old, but Lefty takes aging a little hard: "Lefty realized that he had become one of those older men who slicked their hair back in allegiance to an era no one could remember" (2.7.43). In other words, he desperately wants to revisit his youth. That's fine and all, except he keeps making the same stupid mistakes he made in his twenties, like chronic gambling. This only ends when he has a sudden stroke, which happens to be on the same day that Cal is born. The stroke changes Lefty's life and, in this way, is almost a rebirth of sorts for him.
After Lefty's stroke he stops speaking, and at one point Cal calls him his "Chaplinesque papou" (3.3.93). By this, he means that Lefty has a silent-film-era charisma. He adopts a more carefree attitude, and because he can't speak, communicates solely by writing on a chalkboard. Cal and Lefty seem to bond more without words, though. "We understood each other without speaking" (3.3.94), Cal says. How do you think they get so close without exchanging a syllable of dialog?
When Lefty dies, Desdemona kind of gives up on life, hunkering down in bed to live vicariously through soap operas (who can resist the appeal of evil twins?). When Cal is born, however, Desdemona bonds with the baby, deciding that she is her favorite from the moment she first picks her grandchild up. But after that, we barely hear from or about Desdemona until she re-emerges at the end of the novel.
Lefty and Desdemona manage to keep their big sibling secret safe until Desdemona spills the beans to Cal. She also tells Cal that he can't tell her story until she dies. We can assume that, by reading Middlesex, Desdemona has finally passed on.