Heat the olive oil in a large pot over medium heat. Add the lamb cubes and cook until browned on all sides. Remove the lamb from the pot and set aside.
In the same pot, add the chopped onion and minced garlic. Sauté until the onion becomes translucent and fragrant.
Add the diced carrots and potatoes to the pot and cook for a few minutes, stirring occasionally.
Return the browned lamb to the pot and add the diced tomatoes with their juice. Stir well to combine.
Pour in the chicken or vegetable broth, ensuring that the ingredients are well-covered. If needed, add more broth or water to cover.
Add the ground cumin, ground coriander, and paprika to the pot. Season with salt and pepper to taste. Stir everything together.
Bring the soup to a boil, then reduce the heat to low and let it simmer for about 1 to 1 1/2 hours, or until the lamb is tender and the flavors have melded together.
Just before serving, stir in the chopped fresh mint leaves. Taste and adjust the seasoning if needed.
Ladle the soup into bowls and serve hot with fresh lemon wedges on the side.
Enjoy your delicious Libyan Soup with Lamb and Mint!