Toss the lamb with the flour, coriander, cumin, ginger, allspice, cinnamon and 1 1/2 teaspoons salt in a large bowl.
Heat the oil in a Dutch oven or large, heavy-bottomed pot over medium-high heat until shimmering. Add the lamb, in batches if necessary to avoid overcrowding, and brown well on all sides, about 6 minutes per batch.
Add the onion and garlic to the pot and cook, stirring, until the onions have softened slightly, about 3 minutes. Add the tomato paste and cook, stirring, for about 1 minute. Add the pomegranate juice and scrape up any brown bits from the bottom of the pan. Add 2 cups water and bring to a simmer. Cover, reduce the heat to low, and cook at a bare simmer, stirring occasionally, for about 30 minutes.
Add the carrots and turnips and continue to cook, covered, until the lamb is tender, 45 minutes to 1 hour more. Stir in the cilantro and parsley and season with salt.