Heat the olive oil and butter in a large pot over medium-high heat until the butter melts.
Add the chopped onion and sauté for 3–4 minutes until softened.
Stir in the minced garlic and Italian seasoning, then add the orzo and cook 2–3 minutes, stirring frequently to lightly toast the pasta.
Pour in the chicken broth, lemon juice, and heavy cream and bring to a gentle simmer. Reduce heat if it starts to boil vigorously.
Cook uncovered for about 10 minutes, stirring fairly often, until the orzo is tender and the liquid is mostly absorbed. Adjust the heat or add a splash more broth or cream if the pasta is cooking too quickly.
Stir in the shredded chicken to warm through.
Remove the pot from the heat, stir in the Parmesan and baby spinach, then cover and let sit 3–5 minutes until the spinach wilts and the sauce thickens.
Season with salt and pepper to taste and serve immediately.