Heat oil in heavy large pot over medium-high heat.
Add onion, potato and carrot and sauté until vegetables begin to soften, about 5 minutes.
Mix in curry powder and cayenne and stir until fragrant, about 30 seconds.
Add broth, tomatoes with juices and lentils and bring to boil.
Cover pot, reduce heat to medium-low and simmer until lentils are very tender, about 45 minutes.
Season soup to taste with salt and pepper.
(Can be made up to 2 days ahead. Refrigerate until cold; cover and keep refrigerated. Before serving, re-warm soup over low heat.)