Heat 2 tbsp vegetable oil in a large pot over medium heat. Saute onion in the vegetable oil for about 5 minutes until golden.
Add in the lamb to the sauteed onion and sear until brown. Add in turmeric, salt, pepper and cinnamon to the lamb and onion.
Stir in the tomato paste and mix well.
Pour the water and bring the stew to simmer. Let the stew cook for about one hour and 30 minutes until the lamb is fully cooked.
Meanwhile, heat the remaining 3 tbsp vegetable oil in a pan over medium heat. Fry the eggplants for about 5 minutes on each side until they are soft and cooked.
Once the stew is cooked and the lamb is tender, pierce the Persian limes with a fork and and add them to the stew. Let it simmer for 10 minutes.
Add the fried eggplants to the stew and simmer for another 5 minutes.
Heat some olive oil in a pan and fry the tomatoes for about 4 minutes on each side.
Serve the stew with tomatoes and white rice.