Heat oil in a heavy 12-inch sauté pan or high-sided skillet over medium-high heat. Add onion and cook, stirring frequently, until lightly browned, about 3 minutes. Add lamb, garlic, and red pepper flakes. Cook, stirring frequently, until meat is no longer pink, about 2 minutes. Stir in tomato paste and cook 30 seconds more.
Stir in broth, salt, and water. Bring to a boil over high heat. Stir in pasta and cook, uncovered, over medium-high heat for 2 minutes. Add zucchini, cover, and cook for 3 minutes. Uncover and continue cooking, stirring frequently, until pasta is just short of tender. (It usually takes less time than indicated on package.) If mixture becomes thick before pasta is ready, turn off heat, cover, and let sit until pasta is tender but still firm, usually no more than 2-3 minutes.