Bring the chicken broth to a boil in a large saucepan over medium-high heat.
Add the orzo to the boiling broth and cook until just tender, about 7 minutes, stirring occasionally.
While the orzo cooks, whisk the egg yolks in a large bowl until slightly lightened in color.
Slowly drizzle 1 cup of the hot broth into the beaten yolks while whisking constantly to temper the eggs; the mixture should become warm but not scrambled.
Reduce the heat to medium, then pour the tempered egg mixture back into the saucepan, whisking frequently; cook until the soup thickens slightly to the consistency of heavy cream, about 5 to 7 minutes.
Stir in the Meyer lemon juice, then add the shredded rotisserie chicken and cook 1 to 2 minutes more until the chicken is heated through.
Season to taste with kosher salt and black pepper, then remove from heat and serve warm.