Dice the onion and carrot and mince the garlic. Rinse the lentils until the water runs clear.
Heat the oil in a large pot over medium heat. Add the onion, carrot and garlic and cook, stirring, until soft, about 6 minutes. Stir in the tomato paste, cumin and smoked paprika for 1 minute.
Add the lentils and broth. Bring to a boil over high heat, then lower to medium-low and simmer, stirring now and then, until the lentils are completely soft, about 18 minutes.
Blend the soup smooth with a stick blender, or carefully in batches in a blender with the lid vented.
Stir in the lemon juice and salt, then taste and adjust.
Serve topped with a spoon of Greek yogurt. It thickens on standing; thin with water when reheating.