Warm the coconut oil in a heavy pot over medium heat. Brown the lamb in small batches, then return it all to the pot.
Add the onion and garlic and stir for 3 minutes. Add the oregano, water or broth, salt and pepper.
Cover and simmer gently for 60–75 minutes. Add water as needed to keep the ingredients partly covered.
Add the potatoes and pumpkin. Simmer for another 20–25 minutes, until the lamb is tender and the vegetables are soft.
Check several of the thickest lamb pieces with a food thermometer; for this stew, aim for at least 165°F. Continue simmering until the lamb is fork-tender and the vegetables are soft. Cooking time is only a guide.
Cook and store with care
For this stew, cook the lamb to at least 165°F and until fork-tender. Check the thickest pieces with a food thermometer.
Refrigerate leftovers in shallow containers within 2 hours, or within 1 hour above 90°F. Keep the refrigerator at 40°F or below. Use leftovers within 3–4 days or freeze them. Reheat to 165°F with a food thermometer.