Heat the olive oil in a large pot or Dutch oven over medium heat. Add the onion, carrot, celery, salt, and several grinds of pepper. Cook, stirring occasionally, for 8 minutes, or until the vegetables are soft.

Stir in the potato, garlic, cumin, and cayenne and cook, stirring, for 1 minute. Add the lentils, broth, and 1 cup water. Simmer for 30 minutes, or until the lentils and potatoes are soft.

Remove from the heat and use an immersion blender to blend until mostly smooth. (Alternatively, blend the soup in an upright blender.) If the soup is too thick, add the remaining 1 cup water.

Add the lemon juice and season to taste with more salt and pepper as desired. Ladle into bowls and serve topped with a drizzle of olive oil and chopped fresh parsley.