Preheat your oven to 325°F (163°C).
In a small bowl, mix together the minced garlic, chopped rosemary, olive oil, Dijon mustard, salt, black pepper, and lemon juice to create a marinade.
Rub the marinade all over the lamb shoulder, ensuring it is well coated. Let it marinate for at least 30 minutes at room temperature or refrigerate for up to 4 hours for more flavor.
In a large oven-safe pot or Dutch oven, place the quartered onion, chopped carrots, and celery at the bottom.
Place the marinated lamb shoulder on top of the vegetables. Pour the chicken broth around the lamb.
Cover the pot with a lid or aluminum foil and place it in the preheated oven. Roast for 3 to 3.5 hours, or until the lamb is tender and easily pulls apart with a fork.
Remove the pot from the oven and let the lamb rest for 10-15 minutes before slicing. Serve with the roasted vegetables and pan juices.