Warm oil in a large pot over medium-high heat. Sprinkle lamb with salt and add to pot. Cook, turning often, until brown on all sides, about 8 minutes total. Transfer to slow cooker.
Add onion and garlic to pot and cook, stirring often, until softened, about 3 minutes. Pour in broth and juice and bring to a boil, scraping up browned bits from bottom of pot. Pour into slow cooker; add orange zest and cinnamon stick. Cover and cook on low until lamb is fork-tender, 5 to 6 hours. Stir in apricots and mint. Season with additional salt, if desired. Remove and discard cinnamon stick before serving.