Pat the lamb shanks dry and season them generously with salt and black pepper on all sides.
Heat the olive oil in a large Dutch oven over medium-high heat. Brown the shanks on all sides, then remove them to a plate.
Add the onion, garlic, and carrots to the pot. Cook for 5 minutes until the onion softens.
Stir in the dried oregano, then pour in the chicken broth, lemon zest, and lemon juice. Return the shanks to the pot and bring the liquid to a simmer.
Cover and cook on low heat for 2 hours until the lamb is very tender and pulls easily from the bone.
Stir in the orzo and cook uncovered for 10 to 12 minutes until the pasta is tender. Taste and adjust salt and pepper if needed before serving.