Heat the olive oil in a large pot or Dutch oven over medium heat. Add the onion, carrot, and peppers. Cook, stirring occasionally, until softened and lightly golden at the edges, 6-8 minutes.
Add the garlic and cook, stirring, about 30 seconds, just until fragrant.
Add the smoked paprika, cumin, chili powder, oregano or Italian seasoning, thyme, bay leaves, salt, and black pepper. Stir well to coat the vegetables and cook 1 minute to toast the spices.
Stir in the lentils, diced tomatoes with their juices, vegetable broth, and water. Scrape the bottom of the pot to release any browned bits. Bring to a boil.
Reduce the heat and simmer uncovered for 25-35 minutes, or until the lentils are tender but still hold their shape. Stir occasionally and add a splash of water if the soup becomes thicker than you like.
For a creamier texture, carefully ladle 2-3 cups of the soup into a blender and puree until smooth, then return it to the pot. (Or use an immersion blender and give the soup a few quick pulses.) Stir to combine.
Stir in the spinach or kale and simmer 2-3 minutes, just until the greens wilt and soften.
Remove the bay leaves. Stir in the lemon juice and fresh parsley or cilantro. Taste and adjust salt, pepper, and lemon juice to your preference.
Ladle into bowls and serve.