Heat the olive oil and butter in a medium 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, sun-dried tomatoes, Cajun seasoning, and uncooked orzo; cook 2–3 minutes, stirring often, until fragrant and the orzo is slightly toasted.
Pour in the chicken broth, lemon juice, and cream and bring to a gentle simmer. Reduce heat if it begins to boil vigorously.
Simmer uncovered for about 10 minutes, stirring fairly often, until the orzo is tender and most of the liquid is absorbed; lower the heat as needed to maintain a gentle simmer.
Stir in the shredded chicken and grated Parmesan until heated through and combined.
Remove the pot from the heat, cover, and let rest 3–5 minutes to thicken to your liking, then fluff and serve.