Heat grill to medium. In a small bowl, combine the cinnamon, cumin, thyme, 1 teaspoon of the salt, and ½ teaspoon of the pepper.
Place the lamb in a large bowl, sprinkle with the spices, and toss. Divide the lamb among the skewers.
Grill to the desired doneness, about 5 minutes per side for medium. Transfer to a plate and cover to keep warm.
Meanwhile, melt the butter in a skillet over medium heat. Add the leek and cook until softened, about 3 minutes.
Add the beans and 3 tablespoons water. Increase heat to medium-high and cook for 3 minutes.
Add the corn and the remaining salt and pepper and cook until tender, about 5 minutes. Serve the succotash alongside the lamb.