Heat the olive oil and butter in a large pot or deep skillet over medium-high heat until the butter melts.
Add the chopped onion and sauté 3–4 minutes until softened and translucent.
Stir in the minced garlic and sun-dried tomatoes and cook 1–2 minutes until fragrant.
Add the Cajun seasoning and uncooked orzo, stirring to coat the pasta and toast it lightly for 2–3 minutes.
Pour in the chicken broth, lemon juice, and heavy cream; bring to a gentle simmer.
Reduce the heat as needed so the mixture gently bubbles, then cook uncovered about 10 minutes, stirring frequently, until the orzo is tender and most liquid is absorbed.
Stir in the shredded chicken and grated Parmesan until heated through and the cheese is melted.
Remove the pot from the heat, cover, and let rest 3–5 minutes to thicken before serving.