Trim fat from lamb; cut into 1 1/2-inch (4 cm) cubes. In glass bowl, mix flour, salt and pepper; place lamb cubes and toss to coat. Heat half of the oil over medium-high heat in a saucepan. Place the lamb cubes into the Dutch oven, shaking off any excess flour. Cook lamb cubes in batches until browned; add more oil as necessary. Transfer to plate.
Heat remaining oil in pan over medium heat; cook onions, celery and remaining salt and pepper, stirring occasionally, until softened, about 3 minutes. Sprinkle with any reserved flour; cook for 1 minute, stirring constantly. Add chicken broth; bring to boil, stirring and scraping up any brown bits.
Return lamb and any accumulated juices to pan. Add 2 tbsp (25 mL) each of the parsley, mint and sugar; reduce heat, cover and simmer, stirring occasionally, until lamb is tender, about 1 hour.