Rinse the lentils in a fine-mesh strainer under cold running water, swishing them around to remove dust and debris. Pick through carefully to remove any stones or shriveled lentils, then set aside to drain.
Heat 3 tablespoons olive oil in a large Dutch oven over medium heat until shimmering. Add the diced onion and cook for 5–7 minutes until soft and translucent, then add carrots and celery and cook another 5 minutes, stirring occasionally.
Push vegetables to the sides and add minced garlic to the center; cook 30–45 seconds until fragrant, stirring constantly. Stir in the cumin, oregano, and smoked paprika and cook another 30 seconds until aromatic.
Stir in the tomato paste and cook 2–3 minutes, stirring frequently, until it deepens to brick-red. Pour in the red wine vinegar and scrape up any browned bits from the bottom of the pot; let cook 1 minute.
Stir in the rinsed lentils, diced tomatoes with juices, vegetable broth, and bay leaves, making sure all lentils are submerged. Increase heat to high and bring to a rolling boil, about 5–7 minutes.
Reduce heat to medium-low, partially cover (leave a 1-inch gap), and simmer for 30–35 minutes, stirring every 10 minutes, until lentils are tender but still hold their shape. Add ½ cup broth or water if the soup becomes too thick.
Remove and discard bay leaves, then stir in fresh lemon juice, salt, and pepper; taste and adjust seasoning. For a creamier texture, use an immersion blender to partially blend the soup, then let rest off heat for 5 minutes.
Ladle soup into bowls and drizzle each serving with extra virgin olive oil. Garnish with fresh chopped parsley and serve with lemon wedges and crusty bread on the side.