Bring broth to a boil in a medium saucepan. Add couscous, cover tightly, remove from heat, and let sit 5 minutes. Uncover, fluff, and add carrot, parsley, 2 tbsp. oil, and zest and juice of 1 lemon.
Cook onion in remaining 2 tbsp. oil in a large frying pan over high heat until edges are charred, 10 to 12 minutes. Add garlic, lamb, cumin, cayenne, salt, and pepper; cook, stirring, until lamb is cooked through and browned, about 10 more minutes.
Divide couscous among 4 plates and top with lamb mixture. Mix yogurt with remaining lemon zest and juice and serve with lamb.
Note: Nutritional analysis is per serving.