Heat the oil in a large pot over medium heat. Add the onion and garlic and cook until softened, about 5 minutes.
Add the ground lamb and cook, stirring often, until browned, about 8 minutes.
Add the eggplant, tomatoes, oregano, cumin, cinnamon, salt, and pepper and stir to combine. Bring to a simmer and cook, stirring occasionally, until the eggplant is tender, about 20 minutes.