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 for 3–4 minutes, until softened and translucent.
Stir in the minced garlic, sun-dried tomatoes, Cajun seasoning, and uncooked orzo; cook 2–3 minutes, stirring frequently, to toast the orzo slightly.
Pour in the chicken broth, lemon juice, and heavy cream. Bring to a gentle boil, then reduce heat to medium or medium-low so it simmers gently.
Cook uncovered for about 10 minutes, stirring fairly often, until the orzo is tender and most of the liquid is absorbed. Lower the heat if the liquid is reducing too quickly.
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 until the sauce thickens to your liking, then fluff and serve.