Prepare the following, adding each to the same medium bowl as you complete it: Finely chop 1 large yellow onion. Cut off any stems and fronds from 1 large or 2 small fennel bulbs. Cut in half, remove any wilted or rubbery outer leaves, then finely chop. Mince 2 garlic cloves.
Heat 2 tablespoons olive oil in a large pot over medium heat until shimmering. Add the onion mixture, season with 1 teaspoon kosher salt and 1/4 teaspoon black pepper, and cook, stirring occasionally, until the onion is translucent and the vegetables have reduced in volume by about a third, 6 to 8 minutes.
Add 2 cartons low-sodium chicken broth. Increase the heat to medium-high and bring to a boil. Meanwhile, dice the meat from 1 rotisserie chicken to get 3 cups if needed.
Add the chicken and any accumulated juices, and 3/4 cup dried orzo to the pot. Reduce the heat to maintain a simmer and cook, stirring occasionally, until the orzo is tender, about 10 minutes. Meanwhile, coarsely chop 1/2 head escarole (about 4 lightly packed cups).
Add the escarole and 1 tablespoon lemon juice to the soup and stir to combine. Simmer until escarole is softened, about 2 minutes. Taste and season with more kosher salt and/or lemon juice as needed.