Heat the olive oil in a large skillet over medium-high heat. Add the lamb shoulder pieces and brown them on all sides for even flavor.
Transfer the browned lamb to the slow cooker. Add the diced onion, minced garlic, chicken broth, dried oregano, salt, and black pepper.
Cover and cook on low for 7 hours until the lamb is very tender.
Stir in the orzo pasta and continue cooking on low for 30 more minutes until the orzo is soft.
Turn off the heat and stir in the lemon juice, lemon zest, and fresh dill right before serving.